I (briefly) experienced this recently. I had already checked in online for an intra-Schengen flight and just needed to drop off a bag, but there was no self-service for that, so I had to queue for the regular check-in. I presented my BP and explained that I'm just dropping off a bag, but the check-in agent still asked for my passport and proceeded to check the visa. She was at, at first, not satisfied that I was allowed to enter the country I was flying to and was not impressed when I said "you do realise there are no border controls between these two countries, right? " After checking something on the computer (Timatic, I guess) she proceeded to check me in without another word.

I understand that airlines are required to fly back passengers who are denied entry, but in this case there was nobody to deny me entry and she knew that. So I don't understand the airline's motivation for checking the visa in the first place.

What really takes this from "silly" to "absurd" is that I had already checked in online, so they could really only refuse to check in my bag. I could have just proceeded straight to the gate without that bag.

On the way back there was self-service check-in and bag drop, so I experienced no more of this silliness. Nobody else looked at my passport at any stage.