One practical issue worth flagging is adjustment costs. Cost (losing a leg) = cost (adjusting to one leg) + cost (having only one leg). Since we're told that "the loss of the leg occurred some time ago", the adjustment cost has already been paid. So that's a reason why your premise (2) isn't quite right: sacrificing "another random extra leg" would lead to additional adjustment costs that aren't present in saving the person who is already used to living with one leg. (It's equally a reason why Diamond may be mistaken to attribute to utilitarians the view that "to save the one-legged person... is wrong for almost the same reasons for which it is wrong to cause a person to lose his leg in the first place", depending on how much weight is put on "almost" here, and the empirical question of how the two aforementioned costs compare.)
But it's easy enough to tweak the case. Just make the "random extra leg sacrifice" involve *moving forwards in time* a loss of leg that would eventually occur anyway (perhaps very near their end of life, otherwise), so that a corresponding number of two-legged life-years get converted into one-legged life-years, without changing the number of people who have to go through the adjustment at some point in their life.
One practical issue worth flagging is adjustment costs. Cost (losing a leg) = cost (adjusting to one leg) + cost (having only one leg). Since we're told that "the loss of the leg occurred some time ago", the adjustment cost has already been paid. So that's a reason why your premise (2) isn't quite right: sacrificing "another random extra leg" would lead to additional adjustment costs that aren't present in saving the person who is already used to living with one leg. (It's equally a reason why Diamond may be mistaken to attribute to utilitarians the view that "to save the one-legged person... is wrong for almost the same reasons for which it is wrong to cause a person to lose his leg in the first place", depending on how much weight is put on "almost" here, and the empirical question of how the two aforementioned costs compare.)
But it's easy enough to tweak the case. Just make the "random extra leg sacrifice" involve *moving forwards in time* a loss of leg that would eventually occur anyway (perhaps very near their end of life, otherwise), so that a corresponding number of two-legged life-years get converted into one-legged life-years, without changing the number of people who have to go through the adjustment at some point in their life.