Under which assumptions should Google be forced to "peer into accounts a user has with other services"?
This is not only not enforceable, it would be illegal.
Companies can not be enlisted to do such things governmental agencies are doing. How should a company decide what to look for? Google is not the police and can not be made an investigator just-for-fun. FBI's search engine?!
Also, you need the first factor. Do you expect Google would also send the "password reset"-request, reset the password, use your 2nd factor... Just to be nice to the authorities?
Wild theory if you ask me...