I'm glad someone mentioned live-action sameface, I noticed this happening in sitcoms especially, where the main male characters would look really similar, and the main female characters would have not only similar faces, but the same body types too, only varying in height (and even then, not much). Casting standards, I guess.
Something I think contributes to a lot of anime/cartoons/live action films/tv series same face issues is the "need" (or just desire) to have characters who all fit the ideal beauty standard of one culture. If you're casting/designing characters with that in mind, it's no wonder characters will look the same as one another.
One of the reasons I wanted to explore very different faces, and not get bogged down by making everyone pretty, is to combat my already quite bad sameface syndrome. Let's see:
Old Waste Of Time:

Recent Waste Of Time:

(same 2 characters pictured in both examples, if that wasn't clear XD)
Not saying it's amazing now, but I'm just trying to be more mindful of facial variation. I mean, these two characters above are supposed to be related, but I didn't want them to look like twins!
I find it much more fun to give characters designs based on their personality than by narrow definitions of beauty. Not going to say it's easy though, because it isn't, especially if you learned to draw a certain way!