Fingerprinting works by collecting bits of information about the browser and device to identify users. Couldn’t browsers like Firefox 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.
Taint analysis is a real thing that several papers have been published about, but the implementations aren’t in a state where they could be run in real time without massively hampering performance. Also they’re mostly focused on findings bugs in native applications rather than privacy on the web.