Why can't we wear normal shoes in Tae Kwon Do?

The reason (i think) is mostlybecause you'll slip or scuff up the mats you practice on. It also might be part of their culture, like American's take their hats off indoors... (i know bad example... please bear with it....) Hope my explanation helps! By the way (in my opinion) don't you think it would be harder to kick while wearing shoes?