Sites would then avoid running purpose-built fingerprint scripts and collect fingerprint metrics as a side-effect of necessary activities. Lots of sites need to know window/screen size, DPI, installed fonts, timezone/locale, etc. as a matter of being able to function properly. It would be impossible to know whether a site is also using this information to fingerprint users.

The unsolvable problem is that modern websites are not simply documents but rather full-blown software with web browsers their runtime environments, and you simply cannot enable that amount of power without also enabling the power to fingerprint that runtime environment and thus fingerprint the user.