I sometimes operate media servers that deliver video for several classical pops concerts including Fantasia and a number of more modern Hollywood type movies. The conductor gets a special synchronized video feed with white dots flashing to indicate tempo, colored lines to show when changes are coming up and bar numbers, all superimposed over the movie. The conductor has to speed up and slow down the orchestra in order to match the music exactly (or as close as possible) to the original video. I never change the speed of the video. Some pieces seem to be harder and also require a click track. These are shows that obviously require very close attention to the conductor.
I always wonder if all the orchestra was given a click and a copy of the modified video, if the conductor could just sit down and eat a sandwich. Of course, that is kind of like contrasting watching a DJ that selects mp3 tracks vs someone who can adeptly spin vinyl.
Curiously, I can tell you from listening to the conductors speak candidly, they often consider this sort of conducting much harder despite these added tools. Even when they are playing very familiar pieces like the music from Fantasia, it is very difficult to match it so exactly to the original. They compare adjusting the speed of an orchestra to speeding or slowing a freight train.
With professional orchestras, most only do 1-2 rehearsals before the shows I control video. It is amazing how fast the musicians take notes and adapt to the direction of the conductor. There is almost always a marked improvement between 1st and 2nd rehearsal and the actual show.
I will say that having stood at the conductor's podium at many of the top theaters in the U.S. (while empty) - it is an incredibly intimidating thought. Every seat points straight at you. It is much more singularly focused than a dramatic stage. It definitely has given me (someone with very little musical understanding) a great deal of respect for their responsibilities.