Google has been testing a replacement for third-party cookies
The problem is not the option to place cookies per se. The issue is its misuse which aims to de-anonymize users (in order to place ads).
I don't see how saving the user data somewhere else (in a browser add-on or in the browser natively) is helping here.EDIT:
The official description [https://github.com/WICG/floc], does a better job in explaining the point.
They try to cluster (="cohort") users interests and exchange that with the ad-service. 
This could maybe help to increase transparency and authority over your data as it's saved locally.
But I don't see a way to limit the access to the users cohorts (they even say that themself, see link above). Everybody could access my interests - not just Google and other ad services.
And of course, if you have 1000 categories and some meta information (region based on IP address etc.), you will be able to track down individual users with pretty good accuracy.