Why not? is a better question. It just depends.
To suave modern bicyclers, baskets are a symbol of low-brow, poor-folks, non-serious riding. But we like our baskets, and if that makes us unsuave, that's the breaks..
One reason front baskets haven't taken off on good bikes is that, up to now, they've been designed for bikes with high-rise handlebars and coaster brakes. Those kinds of baskets interfere with cables, and few are the views that bug one as much as sharp bends in fine cables on good bicycles.
Wald, an American bicycle part maker since 1905 (and in the same location in Kentucky since the 1920s) has a new basket that solves all basket/cable routing problems. It works great with normal bikes except those with STI shifters, but something tells me that isn't the market. I/Grant have used a basket almost every day for the past year, and am sold. There are still times when I prefer saddlebags in bad weather, on longer rides, for organizing things. But for short errands or commutes when I just want to throw in some mail, lunch, books, and extra clothing, a basket is hard to beat.
You need a cover, or things will fly out, so we offer a net, too. It's a good system. You can see inside it, and if something soft like a beanie or a pair of gloves is down at the bottom, you can fish it out through the holes.
Rear baskets mount on top of rear racks. Tall rear baskets get in the way when you mount and dismount, so we found a shallow one, which carries lots and doesn't get in the way.
Wald baskets are the cream of the crop. I've seen lots of Japanese baskets, and as much as I like Japanese stuff, I've got to say the Walds have them all beat. They're lighter, carry more, and attach more easily to racks. I think they look better, too. There's nothing at all wrong with the look of a Wald chrome basket.
It is amazing, when you think about it, that baskets of this quality can be made in the United States, and sell for so little.