For exactly those sorts of reasons, I don't expect to apply such a system universally any time soon. In practice I suspect it will only make sense to employ it with a modest number of problematic domains. Currently I use uBlock with javascript defaulting to disabled, manage cookies and local storage, disable referrer headers, etc., but there are still some huge privacy leaks.
On the other hand, it might be possible to devise a solution that works generally but employs white lists or other exceptions for sites that need certain IP-address behavior. That would take a fair amount of effort, but the approach has worked well in similar contexts, such as ad blockers.