Twitter does not "require" a phone number, but they'll lock your account very quickly for "suspicious activity" if you don't provide one.

I imagine Google to be similar.

Yes, and after that they need additional account information for more security reasons, like your second e-mail.

Oh, that's why mine got locked! I've been wondering about that. I hadn't posted a single tweet, yet got notified that my account was locked for suspicious activity.

Same happened to me about half a year ago. When contacting support to get it unlocked, you need to agree to the Google privacy policy. Twitter is lovely these days.

I'm not sure when the last time you checked was, but I cannot currently create new Google Accounts without providing a phone number. It is required.

I literally did it just before I posted the comment. This was on an unactivated Samsung Galaxy Note 5.