I think you're conflating darkness of story with darkness of character. (I think this is what WB is having trouble with as well.) There's
so much compelling story you can do with a romanticized, ideal character in a world of gray. In fact, it's been done before, very recently, except the character's name was Captain America.
I mean, what's more inspiring that a truly
good person who fights and prevails against the darkness? The issue with MoS and BvS was that the dark mood (and general look of the film) overpowered the goodness and light of Superman's character. It pretty much brought him down like seasonal affective disorder. You can't really go too dark in terms of visuals and mood with Superman or Captain America, because everything turns morose and the optimism would stick out like a sore thumb. But there's a lot of heavy stuff that happens in Winter Soldier and Civil War, and there was still space for some lightness and humor. It's not "look how much the entire world sucks, why is he even trying anymore?"
Look, I adore Batman as a character, but not because I relate to him. In fact, we almost have nothing in common besides some detective skills and a stubborn streak. But I adore the character because I find him
inspiring - he has every excuse to be a useless, destructive human being, but he channels it in service to others. Despite his darkness and anti-hero qualities, he's here to
help.
In terms of relate-ability, I'm much more in line with Steve Rogers (you will almost never find anyone squarer than me, I assure you), and I found Winter Soldier and Civil War to be incredibly compelling films because the whole time, he's fighting to do the right thing despite the world telling him otherwise. I work in an environment where it's easy to get bogged down by BS (helloooo government), but my patience and eternal optimism gets me through. I'm here to help, no matter what, and I refuse to let the world tell me how I should do the right thing. Characters like Captain America and Batman are inspiring figures in that fight, because they continue the work even when the entire world is telling them to stop.
I want Superman to be an inspiring figure too, but first you have to give him a compelling story and something substantial (read: un-punchable) to fight against. What needs to be done is finding the right balance, what Superman chooses to do because he's often presented as a God-like character who can do everything, which he isn't, so you have to choose what he can and cannot do in the constraints of the story.