Another excellent question. The current answer in the EU seems to be "you need a phone". My preferred answer (despite being one of the Google guys who designed the ZKP mechanism) would be that the government sends you some sort of plastic card with a chip that does not tie you to a phone. Still fighting that battle.
Yes. However, at some point there needs to be some unforgeable piece of hardware that prevents copying the document. I am a big fan of yubikeys and I wish everybody used them, but the reality is that people lose them way more often than they lose their phone.