Alright, you are making some sense - but here is the problem. You may know the problem exists but with out proof (union shops are like this) and the proof has to be irrefutable - before you can remove a Captain. Now the Captain has to have some character to make it to the rank of Captain as well as pass the tests. Plus we really don't know what Burnsie had over him. Trying to remove the Captain for not keeping his ship clean (highly unlikely) plus Burnsie was going to do what he could to keep his meal ticket in place.
The Allegations of rape could not hold up because the First Mate was holding the crew captive... all of the crews hope was lost. Until they were shown that they could as a group stand up and protect themselves... That was Ish's job. Unite the crew. He showed the crew that they could move up and stand up together. When the isolation barrier broke then the crew started to act as a unit. I really do not find that the story is that far fetched especially when you keep in mind "Power corrupts"
Cause that was what happened to Burnsie... Although I would like to know more about what the Captain was up to...Oh well.
Oh its not that I didn't get WHY. it just seems in this largely corporately controlled universe the owner would have some discretion.
As far as the dirty ship goes that means the first mate and other officers aren't doing their jobs and that IS the captains job(I agree I am reaching a bit here)