What I should have said is that a fighter would make a ship's captain, or captain in general, that is no better than the worst of all other classes and significantly worse than the best choice classes for those concepts. Sorry, I shortened that to "fighters make terrible captains" when the more accurate statement would be, "Fighters, of all the classes, are no better or worse than the worst choices, but, considerably worse than the best choices."
That's clear, but there's a few lingering definitions you're not sharing with everyone.
What criteria makes one character a better "captain" in playing a 5e D&D adventure than another?
From where I'm sitting, a "good captain" should do a few things in play:
- Get NPC's to listen to 'em, which means a CHA bonus (+1-+4, but as long as it's not +0 or -1) and probably training in one of the three CHA skills. Fighters have no less ability to have a high CHA or to get training in Intimidate, Persuasion, or Deception than any other class. So they are the equal of any other class in that regard, with the possible exception of Rogues and Bards. While bounded accuracy means the precise bonus isn't very relevant, 5e does treat rogues and bards as potentially having more persuasive influence and charm than a Fighter. Should a charming rogue or a bard make a better captain than a commander? Is it OK that the fighter isn't equal to the BEST classes at CHA skill checks? Probably open questions.
- Be able to get access to similarly influential NPC's. Mechanically, the only thing like that 5e uses is background features. Fighters can get any background (including the most appropriate for this purpose, Noble), so they are the equal of any other class in that regard.
- Maybe have an entourage. Again, the only thing like this in 5e is background features. Fighters can get any background (including the most appropriate for this, the alt Noble benefit), so they are the equal of any other class in that regard.
A character who can do even one of those three things would rate as a "good captain" in my estimation, and the only thing a Fighter isn't the equal of every other class in the game at here is that they don't have Expertise in Cha skills. It's key to note that this has almost doodly-squat to do with what combat abilities or healing powers or enhancing skill checks, and much more to do with their role in the world, how they're seen by NPC's, etc. A CHA 8 Half-Orc Barbarian Noble can still be a "good captain" because she's got three loyal minions who will get things
done for her and a big axe to do her persuadin' for her. A CHA 18 Half-Elf Bard can be an equally good captain by doing the same thing.
What else would any character - regardless of class - have to do to be a "good captain" in your eyes? And why would those things be essential to be a "good captain?"
Nothing in the fighter class actually makes him a good leader. And, considering that charisma does nothing for a fighter, taking a high Cha actually actively makes him worse at doing his specialisation, which is dealing damage to single targets. Rangers and Bards both benefit from having high charisma.
That's Old Edition Thinkin', son. We aren't in a world of ever-increasing DC's that you must keep pace with anymore, where you only depend on two ability scores and dump the rest, where if you don't have an 18 you don't need to bother showing up because you aren't going to matter. Characters are not monolithic builds that only do one thing. Despite not having a high Cha and not being trained in Persuasion, your druid
keeps making those checks. That's by design. You don't need to be the very best to be competitive.
You want to put your high score in CHA and dump your CON and be a fighter? Go for it. You'll be fine. D&D won't kill you for it or make you fail for it.
A fighter can, possibly, grant a single move action 1/round at most half a dozen times or so per short rest. A wizard can grant a full action to another character, with a bonus to AC and doubling the target's movement at least 1/day and at higher levels, several times per day.
Granting actions doesn't seem to me to have anything to do with being a "good captain." Being in charge of a ship doesn't mean you can make a particular person fight better.
But maybe it's something you want to add. If I were to add it to the list, here's what it might look like
- Grant actions to other PC's. Over the course of a 18-round day (6 encounters, 3 rounds/encounter, rest after every 2 encounters) at 5th level the prizewinner here is a sorcerer with Haste, who can grant a maximum of 3 extra actions in 3/6 encounters for a total of 9 extra actions per day. The closest a Fighter can come to that is to grant an extra attack or half-move in every round in which the Fighter makes an attack for a total of 18 extra attacks or half-moves per day. That seems overly favorable to the fighter (presuming one superiority dice spent on every round), and in practice it'll be more variable, so as a rough measure, lets halve it (the fighter spends one superiority die every other round on average - feels more right): 9 extra attacks or half-moves per day, two per encounter. It looks like, par for the course in 5e, the magic spikes harder (the action is more flexible) but falls apart more easily (Concentration), while the Fighter's ability is less variable, but more consistent (you don't get your entire action, but you'll get to do small things more often). It'd call it mostly a wash - if frequency of offering extra attacks or moves is what you want from your captain, fighters win. If flexibility in the granted actions is what you want from your captain, sorcerers win.
There is very, very little that a fighter can do, outside of single target DPR that another character can't do as well or better.
Looking at the abilities relevant to being a good captain - getting NPC's to listen to you, the ability to get into places of power, the ability to have helpful lackeys, and the ability to grant actions to allies - the only thing a fighter seems to sort of lag on is "I don't have Expertise so I am not THE BEST IN THE GAME at skill checks." Personally, I think I'm comfortable with Bards and Rogues having the highest skill checks in the game, and given bounded accuracy I don't think this is even a huge deal in practice most of the time, but I could see offering 2x Proficiency In Two Skills instead of, say, a Fighting Style if that particular pissing contest was making you feel inadequate.
Put it another way, what can a fighter do that no one else can do better?
Action Surge is the sexiest thing in the game, so there's that.