I agree with you to an extent, and your overall sentiment about there being nothing wrong with super heroes who are just plain out nice guys is spot on.
That said your point sort of falls apart when you start getting into specifics where your by and large equating left wing morality with "what's right" when 50% of the population disagrees with that just for a start. It should be noted that the big trick in a lot of cases to doing genuinely good characters is to have them be good without being stupid. This goes back to the old joke/point that "evil will always win, because good is dumb" in pointing out reality vs. fantasy, or more realistic fantasy situations that get ultra-dark because of it. For example in "Winter Soldier" part of what's wrong with Captain America is that the guy is by definition part of what started as a covert government program. World War II wasn't morally ambigious because of civil liberties issues at home, but because like most things we won largely by being the bigger bastards. We dropped more bombs and massacred more Germans than the Nazis did during the "horrors" they inflicted in London during "The Blitz" thanks to guys like Sir Arthur "Bomber" Harris, who are the reason we won the war (like it or not), people who were decorated heavily by the US and Britan alike, yet were reviled as the same kinds of war criminals as the ones we tried and convicted by the other side. The winners get to write the history books. The purpose of Captain America was actually the opposite of what a lot of people here seem to think, he's a dude who ran around calling Nazis "Krauts" and other slurs that could make it into print to dehumanize them, and he did very much enter the military to act as a weapon against it's enemies. Conceptually he's sort of an answer to left wing isolationist sentiments at the time, and those in the US who were very pro-Nazi (Hitler was an international man
of the year).
Later generations of creators, especially after they retconned away from the whole "commie smasher" days by saying it was never *really* Captain America started using him as a social critic, and a way to attack those that didn't have a left wing idealogy. Forget the whole "William Burnside" thing, it becomes somewhat difficult to reconcile him with the character from World War II he's allegedly still supposed to be.
What's more look at what he did in say "Winter Soldier" where he destroys the three Helicarriers at the end. Okay, granted, maybe him being as pessimistic as Nick Fury doesn't work (they exist to play off each other to an extent, even in the comics, we have two separate characters for a reason), but when he wrecks these weapons as opposed to simply disabling them so Hydra can't use them, he goes from being "moral" to "stupid" especially in a world where things like Hydra exists, and the planet was already invaded by aliens once. It's a case where the writers lust for smacking down the US military/industrial complex trumped any kind of good writing for the character.
What's more while Captain America shouldn't be quite as jingoistic as he is in the "Ultimate" version, one point that version does make is that realistically Cap *would* be invading Iran, Iraq, North Korea, China, Russia, and other places opposed to the US. Indeed part of the point of Captain America, and him being "super" is specifically that he can be dropped behind the lines of places like that and say taken down Iranian nuclear programs, or thwart the schemes of the KGB or Kim Jong Un's tech divisions, without actually having to send in the military... and if they DO send in the military, he'd be right there with them. I mean let's not forget the whole "War On Terror" did start with an attack on US soil, against both military (The Pentagon) and Civilian targets. Properly Captain America would be critical of say The Bush administration for war profiteering, but he'd be just as critical of the left wing stupidity in how to conduct a war and not focusing on a practical method of winning... and yep, in wartime Cap would dehumanize his opponents, and start screaming racial and cultural epitats, not because he's racist, but because it gets under people's skin, and also makes it easier to brutalize people you dehumanize. If you think that doesn't sound like Captain America, then you don't know Captain America, as both him and Nick Fury used terms like "Krauts" and the like for the Germans for the same reason, he wasn't racist, he was just a warrior who knew what he was doing.
That said, the bottom line is that a character like Captain America was created largely for military-type stories and to focus on duels between nations and such. A lot of what causes the concept not to work is when you start involving him too much on a domestic level, which inevitably leads to the writers (currently dominated by the left wing) using him to make very one sided political points which don't always work for a character who is by definition the embodiment of America's military industrial complex, and using overwhelming force for the right reasons (with right being American principles, or the defense thereof).
In short Captain America should be a nice guy, but he shouldn't be dumb about it, and in writing this character in particular it's important that he doesn't become an embodiment of one side of the political spectrum, like he has been for the left wing. Right now Captain America has arguably become a parody equivalent to if he was say a defender of the upper 1% of American society, and spent all of his time punching people in the name of economic theory on behalf of bankers and corporations. Socially Captain America should be VERY militant, but he should also be someone who doesn't exactly act as a tool of the upper class either. When it comes to more social issues, gay rights, racism, etc... he doesn't belong there even if he's long since been used in those kinds of stories by those with an agenda. Those kinds of issues are things he as a super hero is supposed to exist above, as that is exactly the kind of garbage people read comics to get away from.
See, right now I think Captain America should be say punting Kim Jong Un and his ilk, much like his old "Hitler Punching Days", along with the regular super hero stuff. The problem is left wing writers and their "peace at any price" agenda prevents them from acknowledging any group as a real enemy of the US, and treating it that way, and honestly that kind of enemy (originally the Nazis) was what Cap was intended to fight, and arguably be a counterpoint/shaming influence on people like the current left wing who refused to accept those threats, or believed the US should stay out of such events and remain isolationist/it's their own business. Cap was designed as "the guy who goes to war" *NOT* as "the guy who whines about wars and tries to undermine them".
