Haha, of course not. There are tons of attractive girls who don't model, either cause the chance never came up or they have no desire to. And there are some unattractive girls who do it (not making it big time, though, haha).
If hypothetically (and this is very hypothetical, since I'm shortish and have short legs, haha) someone told me I could model, I'd probably think they were trying to get me to buy something, LOL. And if they weren't, I still wouldn't. I would model for someone I knew who was a photographer or something though.
Not all attractive girls model, I'm sure, but I know plenty who do. My sister, my best friend, and a few other girls I know have been approached by agents and have taken advantage of it. None of them are famous, but they've modeled for Victoria's Secret and similar companies.
Most models aren't even attractive in my opinion. They're just tall and skinny. Take off all their make-up and they look like you're average girl walking down the street in which you probably won't even glance over at them.