Is the design decision for different frequencies in PAL and NTSC related to the AC mains power frequency?
Yes, it is related.

In early TV implementations, it was not easy to remove all of the AC line ripple from the DC power circuits that drove the CRT, and this resulted in a slight variation in intensity from top to bottom. It was found that if the vertical frequency of the TV signal was the same as the power line frequency, these intensity variations would appear in the same location on every vertical sweep, effectively causing them to "stand still" on the screen, and this was much less objectionable than having them drift up or down.

There are also sources of RF noise that are related to the power line frequency, and the visual artifacts caused by that kind of noise also stand still on the screen.