I'll just throw in for arguments sake - ascent is an aerobic task for work, but an aerobic + anaerobic task for competition.Excellent description and analogies TreeSpyder! A long time ago I watched my friend a 23 year-old woman take a test to qualify for a lifeguard job. She swam against four younger men just out of high school who were the area's top competitive swimmers. The test was swim 4 lengths of a 25 yard pool under a certain time. At the start of what turned into a race the young guys powered forward aggressively with impressive speed. My friend locked into her superb freestyle stroke as if she was making no effort. She was behind but closing in by the third lap, she beat them all by more than half a pool's length. They were quite surprised that the chill looking "old lady" completely destroyed them ;-) She didn't end up taking the job, better opportunities came up.
I think of rope ascent as vertical swimming, it's a whole body effort, core, legs, arms, everything in smooth synchronization. As TreeSpyder alluded to, the heart and lungs are the limiter, if your chest is exploding at say 60' on a long ascent you'll have to slow down.
For work, one should stay aerobic because the lactic acid buildup bears on the remainder of the climb, affecting efficiency and safety. Shorter and/or moderately-paced steps are best.
For competition, one needs to get up the rope in 10-30 seconds as fast as possible. The lungs don't figure into it because punishment is fine for a limited amount of time. What really matters is whether the first step can be big and fast. If it can, then so can the second, etc.