I don't think he can't prove who he is. He is, after all, the same person. Rather, he can't verify to the service provider that he's the same individual that they have on file, despite being the same bag of flesh and bones he always was. And that is absolutely the service provider's fault.

Blaming him instead of Amazon would make sense if Amazon allowed you to have an MFA backup, or recovery codes.

I use Authy to backup my MFA codes, this works fine for amazon.

When I switched providers and phone at the same time I used my billing address as well as my CC to confirm my change in billing address.

Ensuring I can proof who I am is my responsibility.

You are responsible to ensure your identity. Make sure you backup your 2FA codes.

You can try and shift the responsibility but why would they be responsible for your shit?