The frequency of the power grid is a great compromise.
Make the frequency higher and you get smaller (read: cheaper) transformers and (somewhat) smaller generators and motors. But, you get higher hysteresis loses in the transformers' cores and higher radiative loses in long power lines as well.
The above consideration about 100 years ago ended up with the conclusion that frequencies 20-100Hz are OK-ish. US engineers started using 60Hz as they liked the number for being the same for other time divisions (seconds vs minutes vs hours). European engineers (1-2 years late to the party) liked 50 Hz better for being a multiple of 5 and 2 only, just like other unit divisions they used.
Other, independent power grids use other frequencies (like Swiss railways at 16Hz) because they fit their purposes better.
Skin effect is not really a consideration as most power conductors are made out of a number of smaller wires for mechanical reasons anyway.