As much as you may consider it your human right to open thousands of new untraceable accounts per second with full functionality at zero cost, humoring you requires bending over backwards and resorting to a cat-and-mouse arms race of probabilistic anti-spam and anti-bot techniques. As the adversaries get good, it becomes more and more attractive to just require a phone number (and block well-known bulk suppliers of anonymous phone numbers like Google Voice, Twilio, and Flowroute).
I think this is actually a pretty reasonable arrangement. Someone motivated to stay pseudonymous can obtain a handful of extra phone numbers in a way that would take some effort to connect to his real identity. It's better than drivers license scans or credit card verification.
I think the only realistic alternative would be a proof-of-work scheme. This could protect privacy better, while still making it inordinately difficult to overwhelm a site operator with millions of pseudonyms for the same person. But there are no real standards here. More people have SMS than BTC.