High apm is required, yes. But most people push it by pushing it through spamming 1-2-3 (groups of your army). There was a pro player who didnt do it and he was around +- 70 APM.
It would be interesting to see what percentage of a pro player's APM is actually useful. Like you said, most of the time they are spamming buttons to keep their momentum up.
There is a replay analyzer that attempts to figure this out, generally the effective APM will go up during a fight, but the players will keep the APM fairly high even when the eAPM is not high just because it is easier to go from many useless actions to many useful actions than few useful actions to many useful actions.
I think they are doing it to stay "warm". E.g. if something happens that the fingers can react quick and you don't need a "warmup" time.