Nixon's poor showing during the TV debates against Kennedy was about a lot more than just his five o'clock shadow. He had also just gotten back from the hospital and wasn't entirely recovered. Not to mention the fact that Kennedy had put a lot of work into his appearance and Nixon didn't. All these things were at play here.
Similarly facial hair isn't the only thing that's changed since television, but that's besides the point. And I'm sure that fashion and the times play a part in it too, but the fact remains that the reason politicians don't have facial hair today is for purely PR reasons
. And you'll notice the minority of modern politicians, and almost no major ones do.
Ceci n'est pas une pipe.