On the non polarized plugs. Until the 50's or so they were common. Now the issue is that many many of the things plugged into them (e.g. old radios, appliances etc.) had the metal chassis directly tied to one side and either no transformer or transformer input side tied to the chassis. So, the chassis could easily be hot..... Now all these appliances had plastic cases and plastic knobs etc. so in normal use no issue. Now, suppose a plastic knob broke and the metal shaft for the volume control etc was tied to the chassis? Or if a tube went bad and you were going to see which one took off the back, grabbed the chassis, or decided to turn the volume up after the knob fell off. If the chassis was tied to hot side (50/50 chance) you could be in for a big suprise!!!
Even worse, if the first time you tried this the chassis was indeed on the neutral side, no issue, then plug gets reverse, grab the chassis or knob again, no problem right? and then the big suprise
The advent of the polarized plug fixed the problem, the chassis if connected to a line lead was tied to the neutral, so as long as the outlet wasn't miswired usually no problem.
Then came grounded plugs with a requirement that the chassis, exposed metal be tied to the ground lead with a lead longer than either hot or neutral and neutral couldn't be tied to metal chassis or exposed metal.
Then came the double insulated stuff that can have a two pronged polarized plug.