Because reading a radio signal from the chip was too easy?
Yes, they are really cheap and the law (here in Sweden at least) requires all outdoor cats to be chipped. So the cat is probably already chipped anyway.
Even if for some reason you didn’t want to chip your cat (you should absolutely chip your cats and dogs) it would be trivial to just put a tiny receiver in something that dangles off their collar for the door to communicate with.
Personally don’t want to leave collars on my cats, I also don’t let them outside much though beyond our patio.
Chips are implants that go under the skin. Most civilized places require pets to have them in urban places.