If you look back at Chrome's original announcement about phasing out third-party cookies, they are explicit about replacements like FLoC being how it happens:
"After initial dialogue with the web community, we are confident that with continued iteration and feedback, privacy-preserving and open-standard mechanisms like the Privacy Sandbox can sustain a healthy, ad-supported web in a way that will render third-party cookies obsolete. Once these approaches have addressed the needs of users, publishers, and advertisers, and we have developed the tools to mitigate workarounds, we plan to phase out support for third-party cookies in Chrome. Our intention is to do this within two years." -- https://blog.chromium.org/2020/01/building-more-private-web-...
(Disclosure: I work on ads at Google, speaking only for myself)
This is nothing but another anti-competitive move from the Google monopoly.
Will FLoC speed this up?
As far as I know, Firefox, Chrome, and Safari are already largely publicly committed to phasing out 3rd party cookies over the next couple years. I guess FLoC might move that deadline up a bit?
But I suspect some critics of FLoC are looking at the proposal as a compromise that we don't need to make. The thinking is, at the point where we have public statements from every single major browser, including Chrome and Edge, that 3rd party cookies are going to get phased out, why do we need to throw the advertising industry a bone? We won this particular fight, 3rd party cookies are going out the door. Now (the thinking is) we just need to make sure that counter-proposals like FLoC and FPS[0] don't reverse the gains we've made.
I'm not completely sure how to characterize Google's recent proposals, but an arguably reasonable take that I've seen online is that Google somehow got peer-pressured into making a very public commitment to remove 3rd-party cookies, that they no longer feel they can back down from that commitment, and that a lot of their recent proposals seem to be attempts to find some way to get out of that deal. First Party Sets in particular are just a very conveniently timed proposal. I suspect this take is at least a little simplistic, but if it is at all accurate then now is a very good time to increase pressure on Google, not decrease it.
So I think we might be in a situation where the onus is on people proposing compromise to prove that compromises will make a difference, because I don't take it for granted at this point that FLoC's acceptance or rejection will change anything about how 3rd party cookies are handled in the future.
[0]: https://github.com/privacycg/first-party-sets