I don't see why I should be concerned about giving my ID and signing to enter a bar.

The only reasons I could see that that they would do this is might be:

Damage/misbehavior in the bar - they'll know who was there.
Drink driving - if you are in an accident on your way home from a bar, they will know you were there.

Either way, it doesn't concern me.

Other countries put video cameras at the doors to bars and record who enter with, and who you exit with, and this is frequently used in sexual assault cases.