I didn't say he couldn't physically handle a ship. I said that the fighter would not be competitive with other captains easily available by the core rules for low level NPCs until the fighter is around mid-level.
Well, certainly this is true if the fighter invests no resources in being skillful. Your example of a fighter had only 2 skill points, which implies that the fighter is a non-human with Int 10. I don't have much sympathy for the position that a fighter has to be 7th level to be skillful if no resources are going to be put toward being skillful - not classes, not ability scores, nor feats.
The pirate also has to deal with managing relations with ports, fencing goods, and not getting himself in trouble with authorities or wealthy merchants. A captain whose only available answers to these difficulties is "kill it or sail the ship" is at a distinct disadvantage, unless the GM is softballing those areas.
You earlier sneered at my suggestion that the reutine affairs of running a ship were the campaign focus of a pirate campaign. Now, you are advancing that the captain has to be able to manage the business/economic end of the campaign as if in a normal campaign those weren't part and parcel of the handwaved away 'dead boring' chores of life - 'swabbing the deck' as you put them. Now all the sudden this isn't all 'dead boring'. A Captain whose only problems are 'kill it or sail the ship' is in no such difficulty. There will certainly be players out there who mean by 'I want to be a pirate', "I want to be good at killing things and sailing the ship." Picking a low skill martial class like Fighter and taking it as a straight class with no multiclassing is almost entirely signaling that is what is wanted. If it isn't signaling that, then you can't complain if you aren't as broadly skilled as someone who took resources that could have been invested in 'kill it' and invested them elsewhere instead.
As for defeating the equal level rival single handedly, surely the Expert classed pirate captain isn't the real rival of the PC(s) nor is it the real rival for the potential build. The real comparison here - unless we are using an improved Expert meant for PC's - is between Fighter and Rogue. It's not at all clear to me that a 10th level Rogue isn't choosing to be a sufficiently compotent martial combatant and a sufficiently skillful expert. One would think if all that was wanted was minimal competence of a low level expert, starting out as a 1st level rogue and then going straight fighter would do the job. In the same fashion, our hypothetical expert could dip for a few levels of fighter sometime before crossing swords at level 10. At the very least, our fighter could be human, have 14 intelligence, and invest in skill competancy through things like Cosmopolitan, Education, or even just Skill Focus (if we are going to use nothing outside of core). Rightly or wrongly, a pure fighter with no intelligence bonus is not meant by the system to be skillful outside of combat.
None of this however suggests that you can't be a 2nd level character who is a 'Pirate Captain', even in core. Even if you try to do an end run around the provisions for character creation by trying to build a skill monkey as a pure fighter with no investment in intelligence or skills, then it still doesn't imply you can't be a 'Pirate Captain'. It only implies that you are perhaps not an optimally built pirate captain if your desire is to be skillful and the challenges that the campaign intends to focus on are those that highlight the value of skillfulness.
This decision would be the equivalent of insisting in 1e that you wanted to be a pirate, but insisted on playing a Fighter instead of a class created specific to the archetype (in the 1e style) like Mariner or even Bandit even though that option was open to you, and then complaining that you didn't feel like a 'Pirate' when you played a Fighter because you didn't mechanically have any particular (much less heroic) nautical or skullduggery skills. Of course you don't; you decided to play a fighter.