Because in a free society, a system that stops crimes half of the time and arbitrarily denies people their rights half the time is considered unjust.
Would it be okay for police to stop suspicious-looking people on the streets and ask them for ID and run background checks if it caught criminals 50% of the time?
I don't understand, if you actually assume that ID screening is actually 100% useless (in reality it probably has some reduction), you wouldn't screen at all yes.
If you disagree with the premise that ID screening is 100% useless, then dig up some evidence of its effectiveness.
Showing your id does absolutely nothing to prevent weapons from getting on the plane. If you are so dangerous that your mere identity is enough to prevent you from getting on a plane, then you need to be arrested.
Identity is extremely easy to fake. If you are planning in such a way that you have a realistic chance of hijacking a plane, getting a fake ID good enough to fool the two-second check at the TSA checkpoint is the least of your problems.
There is some argument that a properly built luggage and human screening system could actually prevent weapons from making it on the plane. But ID doesn't really come into it.
But even if we can't develop a system that prevents weapons from getting on planes, it doesn't follow the id checks would be a suitable alternative.