Some people don't pull up on the pedal. I do. I know this because whenever I try to ride a bike with platforms, my feet try to fly off of the pedals on the upstroke.

That said, if you're comfortable on flat pedals, keep riding them. If you like being clipped in, ride those. There is no right answer.

I don't however, understand the notion that there shouldn't be "cycling specific shoes." There are specific shoes for running, golfing, bowling, hell, for working in a McDonalds.