I am in a similar position (and I was actually considering posting this for suggestions) except the fact I am actually having problems convincing MY OWN TEAM & MANAGERS to use version control and project management tools. And while this might not be exactly what you are looking for (I answered at the end of the post), maybe it can help you understand why some companies are like this.
I've been in this company for 5+ years and before I became the Team Lead, I watched the previous Team Lead trying to do the same with almost no result.
In my case the situation is frustrating since:
a) most of my team members try to avoid taking responsibility every time they are given the change
b) every time someone blows it (and it happens), I am the one taking the blame because the manager (who is a non technical person) believes that one's success belongs to all (him included) and one's error (his included) is the leads fault, thus leading to a)
c) the manager often sets up meetings with individual members of my team to assign new tasks (change functionality and design) on a projects where the entire team works or to take them off the project for undefined period of time and fails to notify the rest of the team (or me, in this case) and to fill in the changes in Trello / Freedcamp
I tried everything I could think of:
- Set up BitBucket teams yet we ended up messing things up because some refuse to commit & push their code
- I tried setting up project management tools (Trello / Freedcamp) but as I mentioned above (c) they seem useless
- Members of the team forget or refuse to change the status of their tasks or fill in new tasks if necessary (bugs, possible issues, etc.) because they think it's a waste of time (after all, if they can keep their notes in a Sublime Text or Notepad, it's OK) therefore leaving the entire team unaware of these things (and this caused a lot of problems in the past). Not to mention no one in UI/UX design filled in anything EVER (artists don't have time for this, they say), resulting in devs working on UI features that were about to be removed or changed anyway. Occasionally, the manager sends some spreadsheets or emails to certain members of the team, leaving the rest out of loop.
- We set up Facebook Workplace to enhance the communication and created groups for all projects, teams, departments, etc. Yet the only group used is the roast one.
- For a while I actually had to manually get archives of the apps on my workstation and manually check every line of code to merge changes. Also, I tried talking to my managers every morning and after every meeting he had with my team members to get all the tasks in order to fill them in myself. All these resulted in me spending half of my time checking other people's work instead of doing mine, thus b) above.
- I ended up setting up meetings with all management staff and explained the situation and as a result, we decided to have stand-up meetings everyday and one meeting at the end of the week, in order to make everyone do their job but in the end, it didn't work.
- I even wrote a common sense practice guide that even included How to on BitBucket, Trello and other tools we are using but people simply ignored it.
After all this time and all the hassle, I came to one simple conclusion - it takes a lot to convince people to play nice and follow some simple guidelines and if they don't really want to, you cannot change this. Leading by example works on people that are ready to accept changes and in this case, when you're backed by the management team or anyone who can actually enforce the rules (although I do consider that it's better to explain your point of view and why do you think things should be like that, even if you are right, enforcing is sometimes necessary albeit unpleasant).
Now to answer your questions:
1) Should I let management know that I consider leaving the company
due to these practices?
NO. Never let them know you plan on leaving untill you are certain you have a new job. It's risky for you since the management will assume you are no longer committed and you are only trying to find some excuses no to do your job.
And if you really want to tell them the reason you are leaving, do it after you secure yourself a new job. And make sure you are not doing it by throwing the blame on the management or your colleagues. If you start blaming others, it can bite you back in the future. Be polite.
2) Or at least let them know that I am growing quite frustrated?
Sure. In fact, I believe this is a good idea. You can also ask them to explain why do they think those practices are a good idea. Maybe they actually have a reason for going on like this and you are missing it. But in the end, don't expect too many changes and certainly, not over night.