I hate shoes and prefer not to wear them when I can get away with it. I use my elliptical barefoot or I wear gym slippers, which are basically thin cloth ballet shoes (no support whatsoever).
I don't have your issues though - I have no foot pain, and I have really high arches. I have no way of knowing if I have no foot pain because I rarely wear shoes (even as a kid I rarely wore shoes) or if I have good feet that allow me to get away with not wearing shoes.
There is a school of thought that claims that many foot problems are caused by a lifetime of overly supportive shoes - the claim is that the tendons and muscles in the feet become weak and unable to do the job nature designed them for. There are many people that are barefoot runners and claim that this 'cured' or 'prevented' problems. I think that for some people with some problems, it may be true that bare is better, but as a general statement, it's hooey and possibly dangerous (note that this is my opinion only - not truth).
I think you'll have to find out for yourself what works for you - everyone is different! You could try a *slow* run (or even a walk) on a treadmill or elliptical without running shoes and see what your feet feel like. If they hurt or show any sign of injury, stop and wear your special shoes. If you find your feet are fine or even are better, then you are one of the 'born to be free' types.
BP