I am with KN. We dance for recreation and not as often as I would like! I don't have an arch problem, but do suffer some cramping the next day If I'm not careful. Hey, no pointing those toes! Pain immedietly.
I have flat feet so wearing heels is difficult for me. I'm also a recreational dancer and typically dance for a couple of hours at a time, maybe once every couple of weeks (not enough!). 2 inch heels are about my limit. I know it is recommended to have a second pair of shoes, say Jazz shoes, for when my feet get tired. However, I don't feel that my dancing is as elegant in flat shoes. The only dance that that works for me in flats is an East Coast Swing. At the end of the night it's worth it. I give my feet a good massage and they are good to go the next day.
Hm, I have flat feet too, and I find that heels are helpful because they essentially create an supportive arch in the shape of your foot when you wear them. Not real high heels are necessary, just up to 2 inches as you say. My feet and legs actually get more tired when I wear flats or sneakers (generally, not just for dancing). I've tried various styles of dance sneakers too, and they all make my feet hurt, probably because they are designed for high arches and so they don't fit me properly.
I know people who dance using orthotics in their dance shoes, so it can be done. One woman I know said her dancing immediately became much better when she started wearing the orthotics because it corrected a lot of poor foot mechanics that were harming her dancing.