I think the main issue with that approach is that they could verify that the person in question is Mary Jane born 1/1/1970 in Texas, but there's no simple way to verify that mj1970@gmail.com belongs to Mary Jane born 1/1/1970 in Texas.
You would need to verify your real-world identity before losing your account which people would really hate if mandatory and nobody would bother with if optional.
Google can ask questions like what credit card providers do. They can ask questions about some of their emails, if the verified person can answer them, then they probably are the owner.
How do they verify requests coming from Police and courts who want data?
People who forgot their login can go to Police or maybe some govt office who can help them to prove their identity and then approach Google.
I am sure Google has brilliant people who can come up with a solution if a law is passed for such things.