It was upheld that refusing to Id yourself is a crime. There are laws against hindering prosecution. Those laws are constitutional so violating them is not covered by the 5th amendment.
All this is about an inquiry during an investigation so yes there must be cause for an officer to ask for your ID. He can’t just go up to random people and ask for their Driver’s License (exception random DUI or safety roadside checks). The inquiry may come during a criminal investigation or a violation of motor vehicle laws.
As to your last of course things aren’t perfect. Criminals get fake IDs, steal identities talk their way out of things. There is a reason for that, they are criminals. Not every crime gets you fingerprinted (I could go into what does but it is different in every state). Although it is against the law to refuse to give your name during an investigation, it is not a crime to not have your D.L. on you, just a minor motor vehicle violation. If you have someone else information you can talk your way out of a MV stop with just a ticket in someone elses name. The only way to stop that completely is to arrest and print everyone who forgets their wallet at home. I don’t think that is a good solution.