There's a lot of reasons why Clark isn't as popular as he used to be. More competition, questionable/bad management for the past three decades, cultural shifts, etc. The lack of consistent, regular adaptations in larger media haven't helped either. But perhaps the biggest hurdle is Clark's own legend. Everything else is easily rectified, or is just part of the natural ebb and flow and nothing the character can't deal with, hasn't dealt with before, and won't deal with again. But Clark's legend? That's a tough mountain to climb.
People equate Superman with some sort of religious epiphany. He's held to a standard by the public that the character has never met, nor has ever tried to. Clark is a good man, but he's never been this perfect ideal that people try to force on him. And even though the reputation of Superman exceeds anything he's tried to be, he's still held to those expectations to his detriment. I mean, many of the complaints about MoS was that it wasn't "inspiring enough." No one tosses that trite BS at other characters, not to half the extent they weigh Clark down with. Sorry, but you're just supposed to be entertained by Superman. He's supposed to be a cathartic escapist fantasy who tackles the crapstick people and problems we can't actually tackle in real life. You're not supposed to look at him and see the face of god. The public has completely unrealistic expectations for Superman, most of which have almost no reflection in the actual mythos, and that's done more damage than anything because nothing that is even remotely true to the character will match what people think they want from him. And the only way to get past that is to let Superman's legend fail and fade until no one cares anymore, which isn't an option. Hell, at this point Im not even sure if the legend *can* fade that much.
Every person out there has a very strong idea about who and what Superman is. And 95% of those people actually have no idea what or who Superman *really* is. Anything you do is going to piss off most of them.
I don't know if this would serve as a solution and even if it did, it'd be messy. But perhaps it's time to get back to the core values of the character; the champion of the little guy, taking on the corrupt politicians and businessmen who abuse their power. Maybe the solution is less alien invasions and more stories about stuff that actually matters. Sure, lots of people will bitch about it but if, in the interests of being "for everyone," Superman isn't pissing anyone off, he's not inspiring anyone else either.