"One reason democracy is hard is that people are very motivated to game your system. That makes being transparent about how it works a fool's errand."

That's a major fallacy you're opening with. If something is important to us (as a society), we will find ways to make it serve us well even when it's under attack. The rest of your post even makes a similar point: the social value of well-working search is greater than the economic value for even the biggest search monopolist on the planet. So why not socialize it?