22AWG wiring in a Lamp (GASP)

I found one of those infamous touch lamps with a bad touch module so I took it in (1st strike against me:NO NO NO and I opened the bottom and the sockets were wired with 22AWG is 22AWG good for 120V use? The wires say "22AWG 90C 300V" I know it was made in china but wow! and the main cord to the wall outlet was 20AWG Double Wow! and gasp
I am going to retoss the lamp back where it came from
So my only question/Theory if the 20AWG line cord had a short would the Circuit Breaker trip or would the cord just burn up? Or if the socket developed a short the 22 AWG Would melt or again would the circuit breaker trip?
Anyway thanks and I am not keeping this

 

The conductors inside fixtures do not have to have the same ampacity as those used for general wiring. Fixture wire has a much higher temperature rated insulation and may operate at higher ampacities than general wiring.

Circuit breakers will trip almost instantaneously on short circuits. As long as no larger light bulb than the fixture is rated to use is installed the lamp is probably safe.

 

The load expected on the fixture wiring is a known quantity unlike the wiring in the walls. This allows the fixture wiring to be a smaller gauge than the premise wiring. As long as the fixture is UL listed you should be fine.

Note, UL is not the only listing agency, but it is probably the best known.