>Maybe the solution should be to have some basic free state-paid email provider for those people. They are not forced to use Gmail specifically (albeit the number of non-sucking and free email providers is probably close to zero).
You don't need to use Gmail. There are a lot of good free mail providers.
Gmail allows users to generate 10 one-time use 2FA codes at a time. Even if you are not going to become homeless, you should generate these and write them down somewhere secure. You never know if your phone battery will suddenly die.