No, you just haven't thought through the implications more than a single step.
The real trick is SEO. These systems will be gamed. Google used to handle this by using its monopoly on search to enforce rules. It wasn't perfect, but it kept the worst spam from being in the top five results for the most part. Doing this self-hosted would mean a million users having to agree to do the same thing to punish spam results, and that does not work.
And then there's the problem of crawling and storing the entire web. Doing this for specific topics is doable. The entire web is not. Not for a home user with limited budget. YaCy's P2P mode might be a way around that, but it's also not really "self-hosted" anymore.
Microsoft dumped tons of money into making the second best search engine, and it's a bit of a joke. This is not an easy problem.