[boomlinde]

With analog TVs, it's the signal source that generates the synchronization signal. For the C64 specifically, like all the home computers and video game systems I know, this is derived from a crystal, not mains A/C. Since you need a pixel clock and horizontal clock at consistent multiples of the vertical draw time, using mains to derive the video sync seems very impractical.

My (basic) understanding is that having the beam move at roughly the same frequency as the A/C current is done to mitigate noise and distortion caused by other appliances, which earlier tubes were much more susceptible to.