I am not convinced this is ever going to actually happen. Google won't roll this out until they are sure that their new solution basically has the same effect for advertisers as cookies, but with a new fancy name with "privacy" in it (when its anything but). Google needs to be forced to spin out Chrome to someone else, it is a clear conflict of interest when nearly every (or every? are there any that haven't?) other…
This isn't Google strong-arming the web. This is Google desperately wanting to turn off third-party cookies, and being told again and again by regulators that they aren't allowed to do so.
If Chrome was made by an independent company regulators couldn't care less if they disabled third party cookies.