A. Browsers successfully reduce available entropy to where users cannot reliably be tracked across sites.

B. Browsers fail at this, and widely available JavaScript libraries allow cross-site tracking. If it's possible to extract enough bits, they will be extracted.

The thing is, if you can't get all the way to (A) then in removing bits you're just removing useful functionality and adding work for browser developers and web developers. Fighting fingerprinting is only worth it if you have a serious chance of getting to (A).

If you think (A) is off the table then I agree a regulatory solution is the best option. Even then, #1, as exemplified by UACH, is still helpful because it makes tracking more visible. If every piece of information you collect requires active work, instead of just receiving lots of bits by default, then it's much easier for external organizations to identify excessive collection.

(Still speaking only for myself)