I don't think it's as prevalent as you think. I have a phone, but filter out websites that require a phone number and provide no other option. I simply "nope out" and move on, because those sites are never essential (at least here in Europe).

I always think it's probably a good indication of the quality of thought that's gone into the underlying system too. SMS is pretty insecure, so if they think that's sufficient for security and provide no alternatives, who knows what else they're doing under the hood.