A cop really isn’t allowed to demand your ID just because you were driving, they are not supposed to have they ability.

They’re not. They’re asking to see your license to operate that vehicle. On public roads. In accordance with the law in that locality.

Many people have IDs or passports that prove their identity, but do not grant them the legal right to operate a motor vehicle. And you’re right: police aren’t (supposed to be) allowed to demand “Papers, please!”