I don't know where you are, but public transport and programs to get people to the polls have existed for a long time. They may not drive, but let them go to a store to buy beer or liquor and see how far they get with that. Or, receive SNAP/WIC benefits. Or Disability, open a utility account...where should I stop. Did you rent a place to live? Did they ask for ID? I sure as hell do when my duplex has a vacancy.
Myth? No, they ask when they're looking for someone. You can be as paranoid as you want, but at some point, you might need the police to be allowed to do their damn job.
From Wiki-
"Stop and identify" statutes are
laws in several U.S. states that authorize police
[1] to lawfully order people whom they reasonably suspect of a crime to state their name. If there is not
reasonable suspicion that a crime has been committed, is being committed, or is about to be committed, an individual is not required to provide identification, even in these states "
en.wikipedia.org