On the other hand, as far as privacy from the end point is concerned, users can be identified regardless of IP addresses. Visit fingerprint.com, you will get an identifier, then connect to a privacy VPN and change servers once in a while. The website will identify you, tell you are the same user visited last week from such location, and the number of times you visited.
Browsers (except Tor) send so much data that accurate identification is possible without IP address. And services could refuse to work if users don’t provide the required information, although that info could be randomized.