This doesn't exactly answer the question, but it does suggest that the key explanatory link is the step frequency.
I would like to propose the following "theory".
The use of one or both arms allows for an increase in "step" frequency. (Why? Don't know. Perhaps for the same reason that speedwalkers flap their arms. Biomechanics. The Dutch Wikipedia refers to a slight increase in "tempo" due to the use of arms.)
Immediately after the start you'll see skaters use both arms, and this is also when we see - I think - the highest step frequency, apparently required for acceleration.
During cornering fast skaters need to increase their step frequency in order not to miss the turn. This would explain the use of at least one arm in cornering. (Some will use both arms.)
Just before the finish you might see skaters trying to accelerate for a final push, also using both arms.
During the straights, skaters will use one or both arms when they feel they are going too slow and need to keep accelerating. Especially using both arms is usually commented on as being a sign of tiredness. But I think the more direct cause is that the skater knows that his/her speed exiting the corner wasn't sufficient and he/she needs to speed up.
So why do many of the top-skaters not use their arms on the straights during longer events? My "theory" might explain this as follows: it would increase their frequency beyond sustainability. Above cruising speed, too much work will go into maintaining the frequency itself as opposed to being used for forward acceleration. A lower frequency (with longer, more powerful strides) is preferred. Hence: arms on the back.