Quick edit: you are certainly right that it will be less direct and more effort than cookies.
Neither Facebook nor Google require third party cookies to function, and I doubt FLoC would make any difference when they can already slurp up so much data that is voluntarily provided by other people without your consent (your address book, for example). Google even goes one step further by connecting your Google account directly to the browser, but there's also a reason why your Facebook login will never expire unless you force it to.
This whole thing feels like paying lip-service to privacy to keep people distracted from the reality that a cadre of 90s/00s tech giants have essentially usurped the web.
Most people on the internet use a web browser developed by a search engine company that evolved into a faceless advertising giant, after all.
How are they serving contextual ads if they don't know what you are doing on different websites if the myriad of trackers they offer to content websites do not track you by third party cookies ?
Not at all.
My browser deletes cookies from any website (by default) as soon as I close the last tab for a given open site.
If the browser itself starts tracking me, my privacy is reduced, not enhanced.