I think the most challenging aspect of gear cutting is in the creation of very small gears, such as those that you find in fine watches. I bet they use computer software to manufacture gears at that small size.
Precision is everything at that small scale in my opinion as metal is not very forgiving if you get a notch wrong here or there. It may mean the difference between whether the piece works as intended or doesn’t.
I think only computer software can guarantee you that level of precision. I suppose there would have to be a high level of quality control afterwards, to ensure that the parts meet specifications and that the gears work together as intended in the watch.