When is it appropriate to use push in connections on typical american electrical outlets?
Code requires the wire to be 14 gauge copper when back-stabbed into a device.
People buy them because stores sell them and they're easy to install. Personally, I blame 14 AWG; I only run 12 with 20A breakers. What is a nuisance trip? ;)

What should I do with wires that are too large for back-stab terminals on a receptacles?