I don’t know the math, and they can certainly occur in late shot clock situations, but they seem to frequently occur early shot clock (keep in mind that they are, by definition, non shooting fouls). You seem a bit fixated on the notion that I have no point if the two things are not completely identical. I mean, fine, fraternal twins, but not identical? And you do not get to have your defense set because in a 1 and 1, you have your rebounders going for the potential rebound. So, no.
I would agree that I kind of wouldn’t mind losing the 1 and 1’s that happen prior to the end game, but I still find 1 and 1’s in the last few minutes to be nerve wracking and pretty thrilling. It’s a moment of being put to the sword, and that’s sports.