In reply to jcw:
Quite a few people in the States and Canada do use it; it is called "simulrapping" here. Our climbing websites are full of debates similar to the one here. A couple was recently killed in Canada simulrapping when one of them went off an end.
Knotting the ends of the ropes should eliminate the biggest danger, which is one person going off a rope end, but still, there are more things to go wrong and higher anchor loads, neither of which is a good thing.
I think it is at least a little faster, which can add up over multiple rappels. I've personally been smoked by simul-rappers on a long series of rappels in situations in which my partner and I were rapping very efficiently in the conventional way.
The rappelling devices used have to have enough friction for controlling single-strand descents, and the additional risks involved means that some kind of rappel backup is arguably more important than in the conventional case.
In bad conditions, there is something to be said for having the two party members together and able to communicate easily and unambiguously, rather than having one waiting up at the top in the dark in a gale wondering what is going on with the first person down.