In reply to GrahamD:
> Half ropes are rated to take a full fall, just not as many as a single rope.
Not to disagree with you, but dropping into pedant mode...
If by "rated" you mean tested then the drop test for a half rope only uses a 55kg mass, rather than the 80kg mass used for a full rope. I can easily find you a half rope which is "rated" to take more falls than a single - eg Mammut Genesis 8.5mm 12 falls vs Mammut Galaxy 10mm 8 falls - but since they are different falls, it's not a valid comparison.
Conversely and contrariwise, it would certainly seem logical to
draw the conclusion that given a half rope and a single rope "rated" at the same number of falls, the half rope wouldn't rate the same as the single if the test mass were 80kg in both cases.
If you think of a rope's capacity to take falls in terms of energy absorption, then a half rope tested with an 80kg mass should take about 70% of the falls it could take with a 55kg mass. That is in the basis that the energy of a fall is directly proportional to the falling mass, but it doesn't take into account things like the recovery times allowed between falls in the tests. Call it a first approximation.
If you now look at some real rope ratings, for the Genesis half rope that would work out at roughly eight falls - which is actually the same as the Galaxy single. To look at it another way, for a half rope to take as many 80kg falls as the Mammut Flash 10.5mm rated at 11 falls, the half rope would need to be rated at 16 55kg falls. In fact the Beal Verdon 9mm half rope is rated at 17 falls, so it's in the right area. As a final comparison, the Mammut Pheonix 8mm half rope rated at 8-9 falls could be expected to take about 5-6 80kg falls - which turns out to be exactly what the Mammut Revelation 9.2mm hybrid single/half rope is rated at.
Pedantry, number-crunching and catalogue figures aside, though, I agree with everything else you say: it's balance of risk vs utility/effectiveness. Like a lot of things in climbing, in fact.