Javascript. Not to remove it, but to make it better from the start. Current JS feels painful to me because it feels like piling hacks on top of a poorly-designed language to make it palatable. Doing it better from the start sounds amazing.
The thing I'm most offended with: about every generation has now dumped their favorite interface pattern onto it, mostly reused from the fancy language of the day. It has become a Frankenstein language without internal strictness or attitude (which had been once a major trait.) I guess, it's the language most disrespected by its developers.
It would have been nice if the original idea to have the web support multiple scripting languages had panned out. That's not a design problem, though - some form of code running in the browser would have been inevitable, and it was considered as a possibility from the beginning - but it seems inevitable in hindsight that one language would have won out and we would have all been stuck with whatever quirks and pecadillos that language had.
Maybe if something like webassembly had come along earlier, we could have avoided all that "javascript as bytecode" nonsense.
I wish Brendan Eich's original intention to put Scheme "in the browser"[1] had succeeded. There was never any reason to invent a new browser language when perfectly good one's already existed.
I'm OP, and this was in fact my response to my question! Everyone else is suggesting these wonderful grandiose economic and social changes, and I just want a strongly typed (or, hell, even a little bit typed) Internet...