That alone doesn't allow cross-site tracking. You need a way to identify that the person on one site is the same person on another site, which is the role the third-party cookie plays. Firefox is eliminating the third-party cookie, and working to eliminate cookie-less fingerprinting techniques as well. Who hosts the information is not the concern.
Good point, that’s a great improvement. I just believe you would still be able to identify and fingerprint individuals across sites if you simply pass data through self hosted solution to 3rd part aggregate