Plugs are polarized for the same reason if it’s a light with a socket it keeps the safety aspect of it correct. If it’s a device that is controlled by a switch you want the power leg to kill the power with the switch, not to open the circuit with the neutral and leave everything inside the device hot. Devices that have no access to the power and no switch I see still come without a polarized plug things like little transformers (wall warts) etc.
That doesn’t explain why a light bulb would come apart though assuming one wired one way and the other wired correctly in a parallel circuit. My only guess is that there had to be some sort of shorting going on between the top of the screw in connection and the frame of the light that was connected to the safety ground that produced heat and thus the crack. With the light lit there was voltage to ground no matter how it was wired. With it off the side that had the threads hot could remain shorting maybe. But Villa said they both failed at one point.
Could be a freak random thing where he just happened to have 3 bad bulbs from two different makers from opposite sides of the world or the bulbs were made in the same place and just labeled differently to fool you into thinking they were American made. He just happened to run out of bad bulbs at the same time he fixed the problem.