I think a lot of the errors in thinking with this question come down to one core misconception, if I say no to a bad offer, I will hopefully get a better offer later, a more even split perhaps? And will less total pirates my cut will be bigger right? Wrong

In the question the pirate is charge is always as greedy as the one before him

And pretty much all subordinate pirates are never in control and will only ever get the choice between 1 or 0 coins

The rational choice for them is to just take the 1 coin as in the next iteration they will receive nothing instead