I'm not a guru on electrical code, but as I understand it...
First, the difference between hot and neutral. In household wiring, you only have one wire incoming from the power company, which is called the hot. The other half of the circuit is formed by the ground, and the neutral wire is tied directly to the ground at each house. The way you get a shock is by grabbing a wire so that you complete the connection to ground. The electricity flows down the wire, through you and into the ground. Or it flows from the ground, through you and into the wire. Back and forth, either way, it doesn't matter; you have completed the circuit. But if you grab a neutral wire, you get no shock, as the electricity can't flow from the ground through you and back into the ground. The only way you complete the circuit is by grabbing the wire coming in from the power company, thus why it's called hot. So hot and neutral really refer to the potential they have compared to you.
As for polarized plugs, as I understand it, the appliance couldn't care less which way the plug goes in, as, like you pointed out, the current is reversing directions 60 times a second anyway. Polarized plugs were implemented for safety reasons. Normally, the hot wire comes into an appliance and goes through the power switch first thing, then continues on through the rest of the appliance and out the neutral. This means that when the switch is off, none of the appliance is "hot." But if the plug is reversed, the inside of the appliance is still hot, so that if you touched it, you could complete the circuit to ground and get an unexpected shock. A lamp is a good example of this. If you turn off a lamp and change the bulb, but the lamp is plugged in backwards, then you could get a shock from the metal ring on the bulb as you screw it in, even though the lamp is off.
Cheers,
Warden