Four words: The Intercept, Secure Drop. A one-way mail (content submission) system that runs exclusively on Tor, and thus can't be supboenated for users' IP address.

While I get your premise due to concerns of law, I think it is entirely feasible - and hinges on execution, marketing ability. We already have IP-hiding technology, whether Tor or Freenet or other such. The concern is "are we good enough yet to make it a sustainable business?"

For sake of example: if a hypothetical competitor to ProtonMail was to offer sign-up and email access only over Tor protocol, it would effectively be safe from police's demands to start logging IPs - thanks to technical measures. The actual difficulty is in the business side: getting enough paying customers to install & enable relevant browser or browser plugin.

Granted, the police could try to force the hypothetical competitor to install malicious JavaScript that would try to gather & leak users' IP address or other identifying information through other means, but that's solvable in the longer run just as well.