> that means the government gets to determine who can access your Google account
This is already the case legally: if you lose a court case, Google will follow a legal order to turn something over to the winner. If you're suspected of some kind of crime, Google will follow a legal order granting the relevant authorities access to something like your Gmail messages.
It's also important to remember that this is a real problem affecting a lot of people: ask anyone who deals with the larger public and you'll hear that it's not uncommon for people to change email addresses after getting locked out of their old one, and that problem disproportionately affects certain groups of people (e.g. the elderly).
What would make sense in this regard is something similar to what Apple does where you can optionally set up a legacy contact who is allowed to initiate a password reset, presumably with time delays and notifications (“your password will be reset in 3 days unless you deny this request”). Imagine an option where you could do something like go to the local public library, DMV, police station, notary, etc. and they could basically login to a special Google form to attest that they did a full photo ID validation to confirm that your ID matched the ID registered to an account. That would be useful for thousands of people and if you made it optional, people who are especially worried about their government could choose not to enable it.