I was thinking this too: the Captain phase is the longest of the phases on BGA (due to having to loop players more than once) and in turn-based can sometimes take a week or so to play through! When you can see ahead that "I am waiting for player A to do the single legal move they can, at which point then players B and C will be skipped, so it will be finally back to my turn...when I will have to do the single legal move that I can" I feel it loses more of the feeling of the game than any gained from seeing your barrels shipped. Most of the time there is a choice so it won't completely remove the phase anyway, it just helps speed up the unnecessarily slow bits.
I don't know how hard it would be to implement, but I'd definitely appreciate the change were it to happen! (I've upvoted the bug report).
[An even nicer change would be if the game can work out if there's any possible difference when there is a choice and automate past it if not anyway (e.g. only two players have goods left, both have the same two types of goods, both can fit all their barrels on the ships and leave nothing behind) but that's definitely more complex to analyse and something you don't want to get wrong, so that would probably be a step too much!]
