Now you described a problem and you asked a very particular question, "how do I care less about this?", and I think you have not received an in-depth how-to on how to actually care less about these things. So let me assume that you are not trying to fix these problems but to find a happy place where you are not fixing them.
So you appear to have a very "type one" personality: if something is not done "the right way" it viscerally bugs you. (Keep in mind that this personality system is deeply flawed and I'm trying to pin you down on it after reading you asking one question on the Internet, I don't really know if you map to any personality on this system and definitely not this one.) Any explanation that you come by as to why you are not fixing these things in the organization therefore needs to tie into those deeper notions about the "right way" to do things and the "wrong ways".
If that's correct then I have a perspective to suggest to you: you are trying to optimize a whole system by optimizing the parts of the system, but that is a wrong way to optimize most complex systems.
Why local efficiency is a bad goal
Let me give you an example: suppose you have a "widget" that needs to be assembled by Alice, tuned by Bob, quality-controlled by Caroline, then packaged for delivery by Doug. Let's say each of those takes 100 minutes. You make each of these people 10% better at widget delivery. It depends a little on the topology of the rest of the work, but you might be surprised that this might only cause widgets to be shipped about 2.5% faster -- one of those four fixes actually improved profits and the other three were wasted. So like imagine the QA department is just understaffed for their work, Caroline is just swamped. You made Alice and Bob faster and maybe they worked together and got the widget out in only 180 minutes, optimal given your changes, but since Caroline was swamped with work she just could not start the new work at a moment's notice, she was working on something else, and she could only start it when her other tasks were finished. Even worse: by making Alice and Bob faster, you probably get very frustrated if they are playing minesweeper with their new 10% time so you yell at them and they start producing even more work, and now Caroline is even more overloaded! Meanwhile Doug spends most of his time waiting on QA so he has developed an elaborate ritual to make it look like he's being productive when really he cannot deliver things that haven't passed QA, so he intentionally packs inefficiently so that he doesn't appear to be doing nothing. He does not improve by a further 10% beyond Caroline's 10%-faster-rate because that would just lead to the same problem as Alice and Bob, someone would yell at him for loafing around even though he cannot do his job because he is waiting on Caroline and he doesn't want someone yelling at Caroline to get him more work to do because dammit she's doing the best she can.
In fact if you spend your time trying to optimize every part of this system you are wasting your time because most parts of the system should be inefficient. I did not mistype that, I did not mean to say "shouldn't."
I work in information apps. At most of my jobs I have built software which lives on web sites and crunches numbers and helps people understand things and build things. I get to talk with systems administrators a lot. And there's something very interesting: our servers are generally very far from 100% load. They are very far from 100% memory load, very far from 100% CPU load, very far from 100% disk load, very far from 100% network load -- any sort of load, we try to stay away from. The servers shout at us when they get to "high" levels of load, where "high" might be 10% load or 25% load or some low number like that. Why? Why wouldn't we just buy cheaper crappier servers? It's not just fatigue, but that's an obvious cost -- and also true in the human dimension, if you run people at 100% load they get stressed and burnt out. But for us with servers, the main reason is latency. If my server is not loafing around doing nothing, I cannot get its attention at a moment's notice, "hey drop everything and give me this answer." And that's also true of humans. You try to keep them occupied and optimized, and then you have an urgent request and they have to delay your existing deadlines to work on those urgent requests. Optimizing them so that they are all occupied by 100% load is a really bad thing. You want (in this topology) Alice and Bob's release cadence to be determined by what Caroline will bear, and if there's more than a week's work for Caroline then you want them to slow down and stay healthy and be idle and available for the drop-anything requests. You want to shuttle the non-urgent emails to them to do when they have this free time.
So the way is not to give up your perfectionism -- that is potentially a great strength for you! Do not live any identity that is not your true identity. But you want to reconcile inefficiency with perfectionism so that you, in your perfectionism, can be comfortable with inefficiency: this is how I recommend doing it. Accept as a point of wisdom that actually an efficient system is not locally efficient and a locally efficient system collapses under random spikes of high load due to nasty latency propagation throughout. You will know one of these organizations by a criterion that a physicist-turned-management-consultant identified, "these plants seem to operate on a three-level priority system: Hot, Red Hot, and DO IT NOW!".
What do you look for instead?
Instead, you want to be trying to identify, "what is the one thing that, if we improved it, we could fulfill more orders and bring in more revenue right now?" You want to find the Caroline of your organization -- it might not be QC after all. And you want to make sure that she is living her best life. She should not be collapsing under stress. The queue of things that she needs to do should be organized and every task in there should be effortless for her to pick up. And that queue should be determining the pace for everything else happening at the organization. You should be pestering Alice and Bob, "hey, while you have this idle-time, is there anything that we can do to make life easier for Caroline over there?" and listening to their feedback. You will learn to love when Bob is sleeping at work because it lets you ask, "oh, I am happy that he feels comfortable enough here to do that, does he have something he's supposed to be doing? no? hm, I wonder why that is..." and maybe you can understand that something has changed in your organization and some new bottleneck exists.
Asking as persuasion
You need to ask questions. Ask them obsessively. And that is difficult because you have this personality of "I know what is correct." If some customer inquiries are getting "lost", you need to ask questions about "how can I make it easier for these things to not get lost? What if I set up an email address that you can forward these to, so that they get stored in an issue tracker and other people with idle time can pick up these issues?" If customer data is being entered incompletely, "what can I do to make this an easier process, so that the customers are basically entering their own data into our CRM so that you don't have to do this thing that we're obviously making mistakes on?" If appointments are not communicated to colleagues in time, "how do we make there be fewer appointments?" People set up meetings for all sorts of bad reasons, the main good reason to set up a meeting is to effectively make a decision when there are multiple stakeholders who have different ideas how it should go. How can we centralize each appointment around a decision to be made, and cancel the ones that do not revolve around a decision? How do we get the "hey I have a public statement and then I want to answer any questions anyone has" type of meetings to happen over Slack where everything discussed can be a matter of public record? And if there really are decisions that need to be made but which are known well in advance but we're not communicating that to the stakeholders who need to make that decision so they can't do their due diligence before that meeting, how can we increase the "personal factor" so that someone who needs this decision has come by their desk significantly earlier, "hey there is no meeting set for this but please let me bring to your attention that we're going to have to get these folks in a room sometime soon to hammer out this decision, we're going to want your input, I would like you to prepare some notes for whenever that meeting happens"...? Or do we need to schedule a weekly "decisionmaker meeting" which 50% of the time will amount to "ok we don't have any big decisions, great meeting everyone!" and the other 50% we will stick in all of these sorts of things?
If you think you know how things should be, the right thing for you to do is not to tell someone how they should be. It is always to ask. You are going to be a great asker of questions. "Please help me understand, why is it this way?" will be your best friend. Because if you're correct and you do have a strategy which addresses everyone's needs, then asking the right questions will cause someone else to come up with that strategy on their own. Everyone always adopts the strategy that they themselves came up with. But often you're not 100% wise -- you have the right strategy for context X, but you are actually operating in context Y, which looks superficially like context X but there is some crucial difference. Asking these questions reveals those hidden needs. "We can't do it that way because that would increase load on Caroline but Caroline is swamped with other tasks all the time."
You are uniquely poised to discover the truth and then to ask people the questions that will help them come to that truth. That is a powerful skill and it needs to be carefully deployed. It needs to especially be deployed with a lot of care about the judgments you are making about your situation.
Just to give another example, you say that people "are lazy." If the question you ask someone is "hey Phil, why are you so lazy?!" you are going to have a bad day. You just slammed a door shut that you needed to remain open. But the correct approach is to recognize that people are something like plants. If you notice a plant wilting you want to ask it, "hey, what do you need that you are not getting out of this situation, do you need more sunlight or more shade, more water or less, how do I change this environment into one where you come in every day to work and say 'yeah I love work, I come in and I know exactly how to kick ass today.'" Because people are intrinsically motivated and you just have to steer that motivation at the right thing.
Someone spends too much time answering questions on Stack Exchange (spoiler alert: it's me, right now) -- why? Probably because they have social needs that are not being met in their normal course of working here. How do we get those people to socialize with each other so that their attentions are focused back on work rather than outside of it? How do we build Eden? That is the question of good leadership.