In A Quiet Place (2018), there is a chance of hurting themselves by stepping on sharp objects, which could make them shout in pain and alert the aliens.
Why did they choose to travel barefoot?
Walking barefoot is quieter than walking with most shoes. Hard soles and rubber soles both make noise (felt soles are quieter but hard to find). Additionally, bare feet allow a person to "feel" their way around more quietly in a way that even socks would disrupt.
That's also the reason for the sand in the picture above. Walking on bare leaves makes noise; walking on sand, even with a few leaves mixed in, is much quieter.