If it's better why isn't that how these sites are run? Wikipedia for example is an anomaly.
It's one thing to have an open source model for software that doesn't necessarily need that level of official organization, but once you start getting into backend infra costs, you can't run that on volunteer labor alone, you eventually have to fundraise for infra costs. If only there were a public or community driven internet... it's too bad the peer to peer models (federation, torrents, etc.) don't work well for real time global communications. Centralized messages are much easier to read and write to.
That doesn't mean such a model can't work or isn't good, it's just much harder, and all for no profit motive.
Realistically I could see a bunch of ex FANGers pooling income into a worker owned coop and starting a tech collective, then maybe handing it over to a 501c3 at some point or just keep it going as a private company without outside shareholders. But someone had to organize all that, and it's not the traditional strong suit of devs.
Fingers crossed though. Would love to see something like that happen.
Also I think people underestimate how much effort goes in to moderating Stack Overflow, and how delicate the entire system is. There's already a whole bunch of Open Source Q&A software out there and I'm sure one of them will work fine, that's not really the hard part, and managing servers is also "just" a matter of spending time. Moderating and managing it all is much harder and more time-consuming; there are people whose ability to hold down a job or finish their homework quite literally depends on being to ask questions on Stack Overflow: there's a lot of incentive to abuse the crap out of it, more so than many other sites.