How to say no gracefully in this kind of team culture

Occasionally I came across posts or comments, people decided to leave their management career and going back to individual contributor (IC) role, due to burnout from regular long hours in cleaning up messes of their direct report's mistakes. I got complicated feeling reading this, as observations from my career are very different, I'm not even sure if that's a good move.

As an engineer, I've experienced in org types ranging from small startup, SME, to large US tech. One of the employers practiced re-org fairly often so I get to work in quite a few teams in single job. So far I'd worked in 8 teams across all employers in my career, these teams can be broadly categorised into 2 types of team culture.

Culture A

1. Whenever you made a mistake in your job, you're the owner and be responsible to clean the mess. This is regardless if your rank is junior, senior, team leader, or even team manager.
2. Sometimes mess is too big or too complicated to be handled by you alone, feel free to raise your hand, people always able to receive help from the team without exception.
3. With helping hand from the team, you're still expected to carry the main responsibility to clean things up.

Culture B

1. If someone made a mistake, and he/she is of relatively higher rank in the team, the person will "assign" the mess cleaning responsibility to others who're relatively lower rank. That seemed to be the norm in those teams, no one made noise about it. (there're exception, not all high ranker in the team will do this)
2. Once the responsibility is assigned to you,
   • you're expected to handle it without affecting your existing assignment's deadline. So usually you'll have to work overtime inevitably. For small ones, impact was usually 1-3 days. The biggest mess I'd seen was 1 month OT in a row.
   • the person who made the mistake usually wash their hands off, knocking off on time while you OT-ing to juggle your existing assignment and the mess they introduced.
3. These mess cleaning responsibility usually:
   • has low learning value: doesn't add much value to your professional skill, expertise, CV.
   • has low/no visibility from skip level: boost neither chance nor pace of your promotion, no matter how often or how well you did it.
4. Compare to Culture A teams, mistakes occurred way more often in Culture B teams. Repetition of similar mistake was not uncommon too.

Personally, once I've concluded my team belongs to Culture B, I would not stay there for long, target to leave within a year, either change team or change job. Still, I haven't figure out the way to turn down such "assignment", without burning the bridge with those who're relatively higher rank in the team. Sometimes I wonder if I've been overthinking... should I just be open "this is not my part"? The stress from breaking team's culture is bigger than I thought. How would you reject such assignment without burning the bridge if you're in a Culture B team?

Note: let's assume the option of reporting/escalating to manager or even director is not viable, due to cultural or environmental constraint. So... my main concern is how to minimise OT for such shit, while working my way out for the next team, without burning bridge (could be up to 12 months, or even longer in really bad market).