I'm not sure why Starting Strength says to do only 1 set specifically, but StrongLifts 5x5 has an explanation and it might answer your question. The basics of it is that Deadlifts works a lot of the same muscles as your Squats and are very exhausting on your Central Nervous System (CNS)
StrongLifts: Why only 1×5 Deadlifts, not 5×5?
Deadlift is only one set of five reps instead of five sets of five like the other StrongLifts 5×5 exercises. This is because Deadlifts take more out of you.Here’s why:
- Deadlifts has each rep starting from a dead stop
- Deadlift uses more muscles than any other exercise
- Deadlift allows you to lift heavier weights than other exercises
And
Keep in mind Squats and Deadlifts work similar muscles. Getting stronger at Squats will get you stronger at Deadlifts. You rarely need more than one set of five reps to increase your Deadlift to 180kg (400lb).