Your suggestion sounds like letting the ”crowd” decide; basically voting on the truth democratically. Religion is (kind of) an implementation, where people can “vote” for the denomination whose truth they prefer. They vote with their feet or with their guns, depending on surrounding historical context.
Letting the “market” decide would probably require some additional mechanisms, like financial reinforcement. Advertising is (kind of) an implementation: the more money you spend, the stronger your signal will be. Alas, it’s an incomplete implementation and pernicious ground truth often has an undue influence.
In a sense we already do. Right-leaning and left-leaning groups already believe mostly non-overlapping sets of “alternative facts”. Each side builds its own narrative not so much because of hate for the other side, but because in aggregate the total amount of misinformation has eroded the potential for credibility of any person or statement that doesn’t come from one’s own “in” group.
In today’s Internet you build your own picture of what’s true. Everything else is noise.
Why can't we peer review this stuff and let the "market" decide what is true. We know that this can work quite well and on average it should lead to better results than the social networks trying to do this themselves.
You can even gamify voting things as untrue - each person could have a page rank of things they have said are false and if they consistently downvote "the other side" for things that are true their voting ability will be proportionally reduced.