I think the trope is less of a conscious choice than the result of a series of decisions by the author.
First, the author wants the protagonist to have broad appeal. Because he is intended to be a reader-substitute, he cannot be unusual in any way that is not unambiguously positive. He can be smarter, stronger, richer, or better-looking, on the theory that every reader wishes to himself be smarter, stronger, richer, and better-looking, but nothing controversial. He is unlikely to be a follower of an unpopular religion, a minority ethnic group, overweight, noticeably old or young, or odd in any other respect, unless the work is explicitly aimed at people who are themselves already in the same situation.
As a result, the hero tends to be rather bland. He's usually a white, heterosexual male in his twenties or thirties, handsome in an uninteresting way, unexceptional except in his heroic qualities.
So the author finds himself with a dull hero. What to do? I know: a sidekick! A sidekick can be eccentric and unattractive, he can be fat, skinny, cowardly, forgetful, superstitious, foolish, really anything, because he is mostly comic relief. The reader is not supposed to want to be him.
But now we have two males wandering the landscape, alone together. That will strike the more liberal readers as sexist and the more conservative ones as gay. So let's add a female.
But the female cannot be comic relief, that would be sexist or un-gallant. And making her a distaff mirror of the hero would be boring, redundant, and rather obvious.
Leaving us with two choices: either she is the Action Chick, kicking ass and taking names, or she is the Smart Chick, supplying solutions to unsolvable problems as and when the plot demands it.
My advice, for whatever it's worth, is just avoid this whole line of reasoning completely. Don't try to make your protagonists "likeable" or "relatable". Make them unique. Make her an old, fat, racist lesbian with one leg and anxiety issues. Make him a superstitious ailurophobe who exposes himself on the bus and never showers. Something different. Something interesting.
