Couldn't a (relatively small) proxy server be set up that intercepts the request, checks URL+cookies against a cache, and makes its own HTTPS requests on cache

Couldn't a (relatively small) proxy server be set up that intercepts the request, checks URL+cookies against a cache, and makes its own HTTPS requests on cache misses? Maybe even whitelist cacheable domains so you reduce how fast it fills? I haven't really caffeinated yet so I may be missing something important here but this seems like a few hours worth of work?