This sounds nice but in practice will backfire. You need the systems to be universal, so that everyone, including the richest, have a stake in wanting to see them improved. Otherwise you'll get a two tiered system where the public versions are trash because they're underfunded and the private versions (what the rich use) are great but also expensive af.
You want things to work like insurance, where everyone pays in but only the people who need them use it. I want Musk to pay a fuckton into Social Security, not nothing at all because he doesn't use it. Even now there's a problem with Social Security in particular because, even though everyone has to pay it, it puts a cap/limit on how much you pay, so Musk currently ends up paying his share in the first day of the year, and his contribution amounts to the same as a teacher or something.
Universal programs with progressive taxation, that's the way. Low taxes at the bottom, high taxes at the top.
IMO the Democratic Party is just an institution. It can be taken over the same way MAGA took over the GOP. I agree a multi-party system would be better, but that requires Ranked Choice Voting and I'm not sure if even regular voting is safe right now (although this is an opportunity to reform voting into popular vote + RCV, since it's clear the current voting system isn't enough to protect democracy). But I digress.
With the current system you need progressives to primary the crap out of corpo Dems. Parties don't have ideologies, people do. Change the people and you change the party. (Incidentally, this is what Project 2025 is trying to do with the state: replace all the government workers who oppose them with Trump worshippers.)