I do not think the time AI used to calculate it's move is equivalent to the time it takes for the animation to finish- so if it's possible it would speed up the combat considerably.
As for keeping track of multiple moving characters at once you are right. The only advantage lost will be the thought process a player does as he sees the each individual character take their turn. That temporary plan usually gets tossed out the window anyways as more and more characters finish their turn.
It's basically trading time watching the AI do their thing vs the time players need to assess their new situation and formulate a plan. Imo it promotes time players are engaged vs passive time.
