The sitemaps standard (if this is the basis) would need to be expanded to support additional metadata / structured data to support this idea.

1. This would be up to sites, to your point, major question would be best way to create incentives.

2. This is solvable via a number of approaches, but the search engines themselves would be mostly responsible for finding the right approach for their business. I know how I would do it.

3. Indeed, which would be the main point of this decentralization, to let search engines focus on their hardest problem.

Edit: would Kagi not benefit from having to worry about crawling / indexing sites?