It really depends on the dog's personality. If you have a calm, laid back dog who would just relax, a basket would be great. If you have a dog who is a bit of a hunter type, and alerts to new sights or smells and likes to chase... bad. If you've got a guard type, who might find a stranger threatening... *really* bad. Even cute little toy dogs make jobs for themselves and they *do* them, so I wouldn't want to put the dog in a position where doing their job might be harmful.
Also, for such little dogs, I'd keep their sturdiness in mind. I was raised around Lhasa Apsos and Tibetan Spanials... cute and little dogs to look at, but they've got heavy bones and a lot of muscle. Ours loved to do *big* jumps (3-4 times their height was about average), climb and play rough games for their size. A more delicate dog would get badly hurt doing what our guys did.
( love Tibetan Spaniels...)
Mostly it would be for thier pleasure and company. My paps are all obedience titled AND have CGC s (Canine Good Citizens) and have never been encouraged to act like brats.
I would still want to secure them in the basket--one thing I have learned about dogs is that NO dog is fool proof---but I do wonder about possibilitys in a fall or a crash.
I have that basket with the metal top and I think it's a good design, but I don't want it on my bars...i don't even think it will fit on my 38 size drop bars..