Broken up, how?
For sites like Youtube, I don't believe it to be possible. Only a company the size of Google can possibly handle that level of data, or a government of comparable girth. Either way, you're not going to get an ideal situation. The only way to really stop that would to remove profit from the equation of running an extremely expensive data operation completely, and in that case you're not going to have anything nearly the size of Youtube, unless the entire modus operandi of the economy changes overnight.
More 'equitable' alternatives to Twitter, however, have already appeared, such as Mastodon. The idea behind them being that there is no singular central server, but rather a a list of hosted communities with the software. The list owner may choose to delist objectionable communities, but as long as it remains hosted on its own server, its users can continue to access it. In this case, they'd only control what is immediately visible on their site, and the information would stay up
Is it heavily flawed in its own way? Of course. But I think the flaws of this system are infinitely preferable to these companies having the near-total control they do now. After all, the crazies of the internet split off to their own communities when people decide enough is enough all the time, and delisting them isn't substantially different to what happens to them now. This just takes direct control of the data out of commercial hands. It removes the ability for these companies to report on activists and outright delete information on the behalf repressive governments, too.
The primary reason for my concern with this is that I don't believe Twitter in its current form can adequately be regulated, and the removal of data from their hands would be an important first step. Like you said, you can't just force them into multiple smaller companies, turn them into a niche or regionalize them. No matter what you do, hundreds of millions will be on their site.
Coming to think of it, this discussion should probably be its own thread entirely. It's tangentially related to AmeriPol at best.