It’s a brilliant puzzler, not bogus at all. They could have said prisoners are brought in once a day or something to get people past the idiotic “But what if he brings in only one prisoner a year!? What if he brings in the counter 22 times and then never again!”, but then they’d find something else to complain about. Eventually the counter will be there to count 44 up lightswitches. It might take a couple years or whatever, but it will happen. “But what if some prisoners die!?!”. These are arguments of an idiot. You have to suspend disbelief a little bit. It’s a logic puzzle. “But suppose the prisoners forget! and screw up the counting and switching!!” “But would a warden really be allowed to set them free? OR feed them to Aligators?”
You’re right, ban all logic puzzles, they’re too unrealistic.