The one piece has a certain appeal because only certain body types can pull them off. Any girl who isn't overweight can look good in a bikini, but only a fit girl with a natural hourglass curve to her body shape can rock the one piece and make it look equally as hot. And on that girl it actually looks better than a bikini IMO.
I have a friend who looks like a real life Jessica Rabbit (red hair and all) and because of modesty she wears a very plain looking black one piece. But because of her natural body shape and the fact that she keeps fit, she makes that one plain black one piece look better than most other girls look in bikinis.
On the average girl, a one piece is bettter looking than a bikini. They are classier, and they hide blemishes and a little too much weight. You can't hide that in any bikini. That's why the movie star women of the 50s and 60s who were mostly plump looked good in them.
And you're not virtually naked in front of strangers. I'm not a girl but that must be a little uncomfortable for most women in a bikini.