If websites implement this, it will effectively make building a web search engine impossible for new entrants. The current players can whitelist/attest their own clients while categorizing every other scraping clients as bots.
If not for other reasons, I can't see how Google a search company can be allowed to push something that can kill competition using its market dominance in other areas like browsers.
Because antitrust has been dead for a while. Chrome is a tool to drive people to Google and Google ads and nothing more.
I will say, I did appreciate Microsoft having a browser engine with IE and Edge, even if the former was notoriously a pain, it gave competition in the space. Unfortunately, that's not the case anymore and everything is either Chrome (Blink), Firefox (Gecko), or Safari (WebKit). And it's pretty clear what Chrome has done once that have amassed a dominant market share.
I'm sure there are Googlers who think they're legitimately making the web a safer place, but I think the real reason is pretty clear if you take a birds eye view.