Polycarbonate is Lexan, so there's no huge benefit to putting plexi over the Lexan--unless your friends like to take knives to your CP.
If that's the case, you need new friends, not plexi.
Most of the arcade manufacturers either screenprinted directly on the metal (Atari, Nichibutsu, some Midway, etc...), or screenprinted the back of thin Lexan (Williams and some Midway) on their dedicated CPs.
Plexi didn't make a real showing until the "conversion age".
It was cheaper to print the overlay cheaply and cover it with plexi.