That will only happen when people can't do the things they normally could anymore on the browser. I was/am expecting it to happen with manifest v3, as I understood it it would break userscripts and make adblocking a pain, so far it hasn't happened so I still haven't bothered switching off Chrome.
Assuming this gets implemented, users might start being unable to access certain websites or services because their identity is deemed "insufficient", which would move them to use a different browser that does not have this.