The Nia technique was designed for bare feet. We move differently than we do in shoes. Using the whole foot in our dance creates more strength, flexibility, and awareness of sensation and proprioception in the feet. 'The foot has 26 bones, 33 joints, and over 100 muscles, ligaments, and tendons' (from the Lin article below) - in other words, feet are made to move, as with any muscles you don't use, certain muscles in your feet will atrophy when immobilized most of the time. I practiced Nia in bare feet for about 13 years without any problems with my feet or knees when I began teaching zumba - with shoes. I immediately noticed knee pain, from hitting the ground harder in shoes than I would in bare feet. The fast, lateral movement aggravated the problem. I found that I had to slowly adapt my zumba to my body in order to avoid pain. So, my zumba class was different than most.
The Nia step comes from tai chi, which is traditionally practiced without a lot of padding on the feet. Even as the music and movement heats up, the contact with the floor remains light and easy. I like to tell my classes that we feel the power primarily in our thighs and core, not by slamming the floor with our feet. That said, some students come into Nia with preexisting foot problems, and their doctors recommend shoes, or they may have diabetes, or neuropathy. You can dance Nia with shoes, there is no pressure to take them off, and, you might consider taking them off during the cool-down to build better balance and stability. Feel free to start slow with bare feet (maybe just walking around at home or in the slow part of class. From the Christine Lin article below on exercising in bare feet: "essentially, you're renewing all the neurological connections you formed as a toddler but have lost since you learned to tie your shoelaces." Welcome home to your body!
For a great story on the benefits of working out in bare feet, see: http://nymag.com/health/features/46213/ The article has amazing artwork, to boot!
Another interesting article: http://www.npr.org/blogs/health/2013/08/20/213882836/golden-arches-human-feet-more-flexible-than-we-thought?sc=ipad&f=1001
And yet another very interesting article (Christine Lin): http://www.theepochtimes.com/n3/117003-doctors-orders-take-your-shoes-off/