There is a difference between Blame and Responsibility.
One of the things you need to be very careful about when thinking and talking about these issues is to not conflate those two concepts.
Blame is about finding someone to say is at fault, to associate a failure with. Responsibility is about owning future outcomes and making sure failure doesn't happen - as well as the internalization that you're the person who determines whether failure will occur.
So here's how the two look:
"Sorry the shelves weren't restocked this morning - I probably should've done it."
... that's Blame. Your voluntarily taking it, but it's still just Blame. It's giving people someone to associate the failure with. You're not saying anything about whether it will happen again, what you're going to change, or anything. You're just giving people someone to associate with that failure.
"I can make it part of my end-of-shift checklist to restock if nobody else has done it by the time I'm about to leave?"
Aka, it doesn't matter who's fault this current failure is. That's not where your focus is. Instead, it's about taking ownership of it getting done in the future. You're offering "This won't happen again, because I'll make sure it doesn't."
So along that front: if you're taking "Blame" for things - who cares? Taking Blame doesn't help. If that's what you're doing, I can imagine you would be annoying to coworkers. But if you're taking Responsibility? Awesome!
And that's the core thing: Good leaders don't blame (or simply take blame) - they take responsibility. Is XYZ a problem? I'll make sure it never happens again. Things went bad because of ABC? I'll figure out some way of making it go better in the future.
Finally, don't conflate Managers with Leaders. Everyone can be a leader. Everyone should be a leader. Taking responsibility and owning outcomes is something that's valuable at every job level.