At first I thought this meant they would use the phone number as a proxy to your personal reputation, which was very troubling, but then I realized that's not the case. They are merely trying to predict whether a phone number is real or fake (fraud detection).
It doesn't sound like an end-run around around anonymity, but more like the way retail stores crunch data to predict personal purchase patterns.
Criminals can spoof the callerid and use your number whenever they want. It's easy to do and happens very often in the UK. Your rating is going to be "scammer" quite quickly if you're unlucky.
It's not a kind of captcha, it's an "account discrimination" system. Everybody who cares about the privacy is affected, not only the criminals, and the text shows why: use the throwaway phone, get rejected at the site.
My point was only criminals would use throwaway phones to register accounts. The only time I've ever used a throwaway was when I left my real phone in a cab.
Your point that "only criminals would use throwaway phones to register accounts" is completely wrong (I'm surprised you haven't even used "terrorists" witch such a line of reasoning). There's no site that I want to give my phone to, and I'm certainly not involved in any illegal activities. Ever heard for privacy in the digital age? Anything you won't protect will be sold and replicated in as many databases as possible.
If some site like Google would insist on the phone number, I'd buy a SIM card only for that purpose.
But now there is a push to even not accept such "for one purpose" phone uses. Bad, awful for privacy.
It doesn't sound like an end-run around around anonymity, but more like the way retail stores crunch data to predict personal purchase patterns.
It's a CAPTCHA for criminals.