Yet Captain America is more popular than he's ever been.
I don't doubt that. Just being in well-received movies, and a lot of them either as a lead or part of ensemble, and getting to be played by an appealing actor like Chris Evans have likely done a lot for a character most people probably either didn't know at all or only knew from comics.
Although, I have a more positive attitude about DCEU Superman than most, it's indisputable that the films he's been in have been divisive and not crowd pleasers. I kind of disagree with Mandon Knight, because I feel like Superman's values aren't unpopular. I also believe Superman (in general, not just DCEU) and Captain America are pretty similar in terms of popularity. When Superman showed up on
Supergirl, for instance, it was embraced. And, in box office terms, MOS did better than CA: FA and nearly as well as CA: WS (CA: CW is a bit more of an ensemble). So, I don't think it's the values of these characters that are obstacles. I think what has been tricky for DCEU Superman has been less what his values and actions are (even Donner Superman killed Zod!), and more how the public in his films reward or validate him and them.
In addition, Superman and Captain America have significant differences that may influence perception. Since Captain American isn't that powerful, there isn't as much expectation that he or his values can have as much of an impact on the world. He is also a regular human being (augmented with powers), so he doesn't have to deal with the complications of being an alien or drawing the kind of cosmic threats that Superman does. With Steve, people can project upon him something that's more attainable: he's a regular Joe who is rewarded with powers for being a good person. It's a Cinderella story. Also, Captain America primarily operates as a soldier. He starts that way, then emerges to work for a new "army" in the form of both S.H.I.E.L.D. and its Avengers. Since his films have only ever shown him as part of the U.S. Army or in the process of leaving those teams, we haven't gotten to see him as an independent agent in the same way Superman operates.
That's exactly the point. He doesn't need to be portrayed as being in the right of it. He can be wrong, he can be naïve. It's a solid hook bc it taps into the power fantasy of wishing you could take action against humanitarian crises, if only you had the power. Superman does, so does he just stand by? I like the idea of a Supes forced to weigh sensible diplomacy against human life. He'd spearhead initiatives and use his influence to affect policy, like in Peace on Earth, but if push came to shove, he'd interfere if it meant saving one innocent. Of course that'd open a can of worms, that's the fun of it. It's enough conflict for one movie and then some.
A lot of
Peace on Earth is incorporated into BvS, interestingly enough, both in terms of its imagery and its ideas. Indeed, all of the ideas you've just presented here are explored in BvS with some exceptions. Part of the reason for these exceptions is DCEU Superman doesn't have enough of a reputation yet, compared to
Peace on Earth Superman who seems like a firmly established and older hero, to be able to have the same kind of influence with the U.S. government whereby he can just show up and propose policy for legislative approval. Instead, BvS explores the same ideas using the hypothetical catalyst that is Nairomi while incorporating other narrative elements from comics like
Birthright (Luthor frames Superman) and Greg Rucka's
Unconventional Warfare (Lois is shot at while reporting overseas to get to Superman).
Any complete exploration of Superman needs to involve exploring the idea that he will always have to walk a tightrope in terms of when and how to use his power, how much to impose his will on others, and recognize that there will always, ALWAYS be someone who hates and fears him for one reason or another, as well as those that love him. I thought Snyder's version got pretty darn close to that, actually.
I do too.