I've also noticed TOM's have become very popular in the wsc community. I assume because they aren't rubber soled so they allow for turns without twisting your knee, and are flat so your heals don't hurt by the end of the night.
I often teach in sneakers if I am teaching a couple or a single beginner. I have Danskins, one that I think are made for walking that I use for every day wear, and their soles are not like dance sneakers by any means but are smoother/slicker than traditional tennis shoes. I have a second pair that I assume were made for zumba--they're flatter and have a slick sole. In fact, they're really too slick for a ballroom floor, so I'm judicious in when I wear them.
Years ago I was having trouble with plantar fatiitis, and I wore tennies all the time, even social dancing. Now I prefer dance shoes for social dancing.
I prefer sneakers for salsa and swing. For some reason I feel a lot more calm wearing them, and I feel like I don't have to do a bunch of crazy stuff if I am just a normal person wearing sneakers. If I am going to be doing some smooth stuff, I normally put on my dance shoes.
I wore sneakers when I first started dancing, but then I tried wearing my old marching band shoes from high school, and those ended up working much better. Now, whenever I dance in my regular tennis shoes, I can hardly move around on the dance floor.
I think it has less to do with the material of the sole and more to do with the treads. As far as I know, my "dance" (marching) shoes do have rubber soles, but the treads are very shallow and almost nonexistent.