If you want to prevent fingerprinting, you need to look at where the identifying bits are coming from. (ex: https://coveryourtracks.eff.org/) The IP address provides enough bits to uniquely identify many users, and when combined with just a few more bits, to identify almost anyone.

TOR is one solution here, which you could potentially also describe as "adding forced MitM to every connection". The proposals in https://github.com/bslassey/ip-blindness/blob/master/near_pa... and https://github.com/bslassey/ip-blindness/blob/master/willful... have different tradeoffs than TOR, with the "TOR is painfully slow" problem being a big one.

If you have better ideas, though, I would be very interested in reading them!