For what it's worth, there are a lot of high-quality dress shoes around now that use thinner, rubber soles. They don't look like the first batch of rubber-soled dress shoes in that they don't resemble Doc Martens. You can't tell them from regular dress shoes except that people can't hear you walking.
I have a pair like that now. I'm sure they'd get good grip on a bike, but I imagine they'd get trashed by road grime and such.