Google could put a toggle in Google Account settings titled something like "Allow anyone who knows my password to log in to my Google account (less secure)." It could sit above a description of the risks involved. It would need to be disabled by default, and it wouldn't help users who don't know about it. It certainly would not fix homelessness in society. But it would do a lot of good for a lot of people!
Would this option lead to some increased number of hacked accounts? Probably, but these would be accounts that explicitly opted in to that risk! I think it's excessively paternalistic to not provide the option. Every life situation is unique, and people know their own lives better than Google does.