Another reason skaters might not do runthroughs at competition is because they have limited access to practice ice at the competition, and their music will be played only once during the practice session, in an order determined by random draw or by skate order.as for your first question, i guess it depends if you are referring to at competition practice ice or normal daily training. at practice ice many skaters won't do a full runthrough to conserve energy for the competition.
So if their music is going to be played early in the practice session, they may not feel that they will be sufficiently warmed up to attempt most of their elements while their music is playing.