The good thing about proof of work is that it doesn't specifically gate bots.
It may have some other downsides - for example I don't think that Google is possible in a world where everyone requires proof of work (some may argue it's a good thing) but it doesn't specifically gate bots. It gates mass scraping.
Things like google are still possible. Operators would need to whitelist services.
Alternatively shared resources similar in spirit to common crawl but scaled up could be used. That would have the benefit of democratizing the ability to create and operate large scale search indexes.
It may have some other downsides - for example I don't think that Google is possible in a world where everyone requires proof of work (some may argue it's a good thing) but it doesn't specifically gate bots. It gates mass scraping.