Yes, we need a better solution.
The problem is exactly that trust isn't equal to identity and that faceless corporations (CAs) endorsed by other corporations (redmond, mozilla, google, etc.) vouching for the identity of websites, forcing you to rely entirely on their "due diligence" and the sanity of their (arbitrary) paperwork backed by very few guarantees any end-user can make use of, ever, doesn't get you what you need. That is, that you have some sort of assurance that you're talking to who you think you're talking to.
Can't blame them for trying: Back then netscape had to start somewhere, and well, they did. The result is something that models a "chain of trust" or a "tree of trust" rooted at the top, which vaguely fits the usual top-down approach in corporations. And for some reason, hierarchical trees tend to be the perennial favourite of programmers. But even six hundred roots isn't doing the world much good. So something needs to change.
I say we go back to the very beginning, and look at the assumptions there. We're looking for trust, not identity. We're also looking for a system that can deal with vague, fluid, changing notions of same. We're looking for something that's useful in the real world as well as the artificial environment of the wage slave-filled conglomerate.
If you wonder about trust vs. identity: The problem is of course that if you don't know the other side in the first place, there's no point in trying to ascertain it's them. You have no prior knowledge to match against how they check out. In the face of that I'll settle for being reasonably sure we aren't being attacked by a man in the middle.
Even so, you only get that ascertained over the connection between you and their front-end. You haven't an inkling what's going on behind the front. It might be a veritable sausage factory. Anyway, I'll leave that aside for the moment, but it's something that too needs to be dealt with eventually.
There are a couple more things that such a system needs to provide, allow, do, and/or explicitly not provide, withhold, prevent from happening, as the case may be. Which ones can you think of?
I have a slowly crystallising notion of where I want to go; though I've voiced it often enough I won't here. Instead, going on the notion that identity is but a sideshow for establishing trust, share your ideas. What can you come up with?