Fingerprinting works by collecting bits of information about the browser and device to identify users. Couldn’t browsers see when a website gets such info with JS and either prevent or ask permission from the user for the website to make HTTP requests to upload such information to the website. Idk if they do something like this already.
And if you are going for anonymity on the web you will be sticking out like sore thumb if you block something. Being anonymous works best when you are hiding in the masses, what you want is alot of computers reporting a similar setup, then if is very hard to pinpoint who’s browser belongs to who. A good example is never using the Tor browser in a maximized window, because then your screen resolution is an fingerprinting factor.