You know, now that I've thought about it a little more, Freakazoid may have been ahead of its time, at least in that people didn't get the connection between being powered by the Internet and being a looney, but it was also very much a product of its time. The premise of a superhero who gets his powers by zapping himself into "cyberspace" is a very '90s thing, as you point out at the beginning. It would have been well past passé by the time the general public was familiar with Internet culture. It wouldn't even work as a parody, because the thing it's parodying would fall in the window of too-old-to-be-current, too-new-to-be-retro. Plus, once Internet memes became mainstream enough for anyone but niche audiences to get the joke, they'd be mainstream enough that you couldn't really parody the phenomenon so indirectly. He'd have to be some guy who goes around making direct references to specific memes all the time. And then everyone would hate him.
Maybe I'm overthinking this.
The upside is, between nostalgia for the source material itself, a better familiarity with the gimmick, the popularity of superhero movies and a general lack of parodies of them, and the fact that dated origin stories fall under the grandfather clause, the time is ripe for a Freakazoid movie. It would have to take some liberties with the concept, like actually be a parody of superhero films rather than just 90 minutes of random crap happening, but I think it could work.