The correct solution to this and a shitload of other problems is a real, national ID program. But there's enough resistance to it in both US political parties that it can't happen. The lack of it causes a ton of stress, over the population, and is a drag on the economy, but we're just never gonna fix it. Instead we'll de-facto have one (or more) anyway, including 99% of the risks that a real one would carry with it that everyone's so hand-wringy about, but without the benefits of the real thing.

It's not ideal, but phone numbers already are how we verify identity online and sometimes offline. There's been other methods proposed, but they've generally been rejected because of concerns over privacy.

I'm not proposing a solution for the real issue, simply a way of making things easier for people who have a hard enough time already.

It already is that, which is precisely why google is using it here. Google is an american private company. Phone numbers have government mandated systems around the world that allow a individual to keep using them even when they lose their phone. Google uses it because it lets governments solve the identity problem in the fashion and to the degree they deem acceptable, and leaves google in the tech business. Some countries have issued ID cards which support encrypting and signing documents. If that becomes more widely practiced, then google could switch to that instead, but until then I imagine they'll keep using phone numbers.