[KayL]

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)

[f00zz]

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.

[bmarquez]

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.