For me, the attraction is four-fold.

Firstly, I design on a computer, so being able to just tell the computer "Take this, and make it" is fantastic - I don't need to print anything out.

Secondly, I can get a significant amount of accuracy that I wouldn't have been able to get manually. I'm designing a car body, and it's expected that a manual process would be, at best, 3mm from side to side. The computer's accuracy is significantly higher than this (I'm aiming for 1mm, but I know that it should be able to get much higher).

Thirdly, it's repeatability - if I need to make 1 'doodah', then manually it would be doable. If I needed to make 10, then it would be a bit laborious - 100, and I'd get really tired of it.

Finally, it's automatic - I don't need to watch it do its thing over many hours, so I can get on with other things while it's doing its thing.