Why plug is polarized in the US? What are the benefits?
It's more than that -- polarized plug make cheap single-pole switches much safer.

For example, look at the extension strip:



With a polarized plug, it is perfectly safe to have a single-pole switch  there-- one just makes sure it interrupts the "live" contact
With a non-polarized plug, one either has to put a more expensive double-pole switch, or to accept that half of the time, powered-off power strip would present a shock hazard. Neither of these options is very good.


It gets even worse with the fuses -- they are single-pole by definition. So if you have something protected by a fuse, and the fuse blows, it better be the fuse in the live wire! And in the non-polarized-plug land, a blown fuse might leave device non-working, but still energized -- which is pretty dangerous.