When I watch a movie, and see a character who's defined by being ugly, or short, or overweight, or old, I wonder how it affects the psyche of that actor/actress.
Certain people are clearly typecast as certain things, and there's no doubt they wouldn't have the same castability if they lost that distinctive trait. But it probably doesn't make it any easier to always show up when they're casting "ugly girl."
Now, it's not the casting directors who are putting them in this position. It's a reality of making movies that you need certain types of people to play certain roles, and they're forthright about what they want in the ads. You don't want a bunch of models showing up to play "ugly girl," unless you also have a pretty healthy makeup budget. So you're basically telling all potential actors, "Hey, only come if you can 'play ugly', and are willing to be thought of that way by us." You also don't want a bunch of people showing up and getting offended at being pigeonholed, being narrowly defined by that one trait.
Of course, "ugly" has different gradations. There are any number of actors/actresses who clean up well, but can also make themselves look ugly under the right circumstances. I suppose that's what you call "TV ugly, not ugly ugly," to borrow a line from The Simpsons, in reference to poor old Moe Syzlak.
But you're still putting yourself in a position where some casting director might tell you that you were "too ugly." That probably wouldn't happen -- they'd probably dismiss you with the generic "You're not right for the part," which leaves your shortcomings up to your own imagination. I guess in this situation you'd be hoping for "You're not ugly enough," which might be the charitable (if blatantly untrue) rejection line they use if they care about whether you leave the casting office with a spring in your step.
I was trying to think of some good examples of "ugly girl" or "fat guy" or "old guy," but not many come to mind. The problem really is, if you start out as that guy, and have enough success at it to become famous, those traits tend to go into remission. No, you can't make yourself younger, but a personal trainer or plastic surgeon can help with the other two.
Okay, let's take Jennifer Grey as an example. When she was cast in Dirty Dancing, I'm sure they didn't look at her and say "Wow, that chick is ugly." Truth be told, she's not ugly at all, but she did have a rather prominent nose for a Hollywood actress, which probably put her closer to the "ugly" end of the spectrum. She was definitely not supposed to be a sexy young ingenue, but rather, a regular girl looking for her prince, in the form of Patrick Swayze and his swiveling hips.
Grey had a rhinoplasty in the early 1990s which was botched, and followed that with a successful one. It was successful in that she's a lot prettier now. But it was unsuccessful in that she is no longer recognizeable as the star of Dirty Dancing and Ferris Bueller's Day Off. There's no great certainty that an unaltered Grey would have gone on to a great career, but the altered one -- even though she was prettier -- certainly did not. In fact, Grey has publicly called the nose job the worst mistake of her career.
Sometimes, you're better off just being "ugly girl," even if it hurts in the darkest moments of sleepless nights.