Here's the thing, your complaints could be made about every single comics character. "but Superman is, I think, *more* human than Cap. He has a wry sense of humour, family and friends that he loves, etc. I think Superman is far more human than Captain America, and this is in part *because* he's not. The fact that he's really not human and yet so very much so is what makes him work"
I disagree. While Cap doesn't have a family, he has the same amount of friends and teammates that Superman does. His character is also more developed because he's had different relationships with different women while Superman has been with Lois for 70 years. Superman is far less human then Captain America. Superman is a messiah concept, he's never been small or weak. Cap has. Superman lectures humanity about it's flaws and weaknesses without understanding them. Superman treats humanity like a child that needs protecting and I often find him conscending. Captain America treats humanity like equals.
"Complicated. First of all I don't think he's that interesting as a person. He's bland (sometimes I think deliberately so) second, by virtue of who he is he gets turned into a political mouthpiece"
Once again, every character. It depends on the writer whether a character is interesting or not. He may be used more as a political moutchpiece but he's a patriotic WWII-era hero. It comes with the territory. But hell, the whole concept of the X-Men is "RACISM IS BAD!"
"not to mention that the provincialism is annoying, I don't care about what America means, I care about what it means to be human)"
Does that mean you hate Union Jack, Captain Britain, Black Panther, Namor, Sabra or any other patriotic character or character that has a primary meaning thread in them? What do you mean by provincialism? Do you want every character to be an international concept?
"Thirdly, he speechifies. I loathe speechifying." In every character? Including your favorites?
"Fourth: He's Batman. Except he's not as smart and doesen't have the gadgets" Not as all-round smart? Granted. But he's never needed all those toys, he gets by without them. Cap and Bats have different fighting styles. Batman is a sneaky detective while Cap is a frontline soldier.
"He's an (admittedly very good) martial arts guy in a team that takes on gods and indestructible robots. I wouldn't mind it if it was explicitly acknowledged that in those cases his job is to be a tactical/leadership figure and not go out and punch gods in the face, but it doesn't."
He's the best unarmed combatant in the MU actually. His leadership while fighting style is part of his character design. The reason he's "Captain" America instead of General or Colonel is because a Captain is the highest level of officer that sees combat. Once you get promoted above the captain rank, you're usually behind the lines. While Captains plan but still lead men into battle.
". Fifth, I hate how people gush about him. That makes me want someone to punch him in the face repeatedly." Are you talking about fans or in-universe? Because fans always gush about their favorite character and in-universe he occupies a very respected position. He's earned the respect and awe of many people.
"Sixth: There is a tendency for him to be put up against a (strawman of) the issue of the day and defuse it by saying something completely meaningless and not acting it" Once again, every character that has ever been written.