@marvomatic Yeah, most appliances want a ground wire. But a polarized plug is important on two-wire cords with things like lamps, especially.
Otherwise, with a non-polarized plug, the lamp is potentially a shock hazard. Basically a 50/50 chance of that, depending on how you plugged it in.
Plugged in “wrong”, the lamp switch turns on/off the neutral wire, leaving the lamp socket base “hot”. Easy to get shocked changing bulbs!
Btw there are tons of older vintage lamps out there still with non-polarized plugs.
Worse, places like Lowe’s still sell replacement non-polarized plug ends, to “fix” older lamps!