You entire premise is flawed since google.com is not privileged in this. It has exactly the same capabilities of setting first-party cookies as every domain.
"But Apple's and Mozilla's moms let them disable third-party cookies" isn't likely to be a winning argument in court when the major Western competition authorities threatened you in advance with anti-trust action.
If google.com isn’t using any privileged position (I was guessing they were, from your comment), then where’s the problem? There’s no antitrust: third-party cookies are a privacy problem, and the browser industry has unanimously decided to remove them, and in fact everyone else has already removed them—Google is last here. The fact that one of the browser providers (and yes, maker of the biggest one) happens to be an advertising company should then be irrelevant—either Google is simply doing things better than everyone else in the advertising industry, or they’re behaving anticompetitively in some other way. But I don’t see how this could legitimately be tied to removing third-party cookies.
I agree that what you say should be true. But it is not, and I've already posted the sources to show it in my first message in the thread. Do you think the sources are fake? Or do you think that all those regulators are just joking around, and when Google does something they expressely forbid, it'll just be laughed off?
As a matter of fact, Google domains do have (or at least used to have) privileged treatment in Chrome: There are special request headers that Chrome automatically includes in requests to Google-owned domains - and only those. [1]
But even if not, Chrome makes all kinds of API calls to the Google backend, independently of browsing. It would be trivial to e.g. upload the browsing history there and associate it with the user's Google account.
I think the argument is that disabling 3rd party cookies in Chrome would not be anti-competitive is Google didn't collect any information about Chrome users.
"But Apple's and Mozilla's moms let them disable third-party cookies" isn't likely to be a winning argument in court when the major Western competition authorities threatened you in advance with anti-trust action.