On medium, when I logged out and saw what sort of experience the site was giving the readers of the things I worked so hard to post there, I stopped posting there.
Last time I tried to create an annoymous account ,they asked for tel verification.
(not exactly when you sign it up but after a few day)
Same. It allowed me to create an account with just an e-mail address, but soon after the account was suspended for "unusual activity" and the only way to unlock it was with a phone number. At this point I gave up.
Had that exact same problem, I emailed customer service via their webform asking what went wrong and a few days later Twitter replied, removing the "suspension"
I think they're just fishing for mobile numbers for targeted advertising identifiers.
After creating an account, you will be prompted to give them your phone number, and afaik, you cannot skip this step