Random searches of little old ladies with Brooklyn accents are indeed a waste of time. However, trying to confirm that the person under whose name the ticket was bought has matching ID to that name serves a useful purpose.
Even if it is a false name, that false name can be a known alias in the intelligence data bank. Since you cannot pay cash and hop on a plane anymore, such a name, even if false, leaves behind an intelligence data trail.
As far as "getting on my ship", yes, every Officer of the Deck aboard my ship knew me by sight but, to get to the ship you had to walk through a restricted area where many warships were docked including carriers with thousands of men unknown to our crew. Nobody walked through that restricted area without their ID hung visibly around their neck. and available for immediate inspection upon request. To do so invited immediate detention for questioning.
That is why, on my last day aboard after turning in my ship's ID card, I required a Master-at-Arms to escort me from the quarterdeck out to the gate of the restricted area.
No visible ID available for immediate inspection upon request - No passage. - No exceptions. - Not even if you were the Commanding Officer of a CVN.
Is that any way to treat a loyal U.S. Naval officer with Constitutional rights?
You betcha.
There are lots of potenial security problems in this country, and a limited amount of resources to protect them. Instead of a providing a false sense of security in everybody having an ID, I would much rather have a real sense of security from active surveillance of suspects, active defense of vulnerable locations in airports or any other infrastructure. Just one simple example, better use of sensors to detect explosives.