Toddlers should wear shoes to protect their feet and to provide comfort when walking around outdoors or in stores, daycare etc.
Barefoot walking is good and beneficial for a toddlers foot development and for sensory motor development.
Although toddlers should still wear shoes in certain situations.
Even in stores there could be shards of glass and other debris on the floor that you cannot see and they could cut their feet.
I've seen that happen to a 2 year old boy walking around a grocery store with his mom and he was wearing just a diaper, shirt and no shoes on a hot day.
Well when walking down an aisle he suddenly stepped on a very tiny piece of glass and it cut his feet some and he started crying.
His mom picked him up and his feet were bleeding and I went over to help and he had a small piece of glass in his foot.
He was okay after we removed the glass and applied a bandage that I had but that's a good example of why toddlers and children should always wear shoes when away from the home.
Outside in areas where it's safe it can be okay for the toddler to go barefoot but when inside stores, daycare's etc they should be wearing shoes.
Shoes provide the toddler and children and even adults with a protective barrier from hazards like hot surfaces, sharp objects and inclement weather.
Shoes also help keep toddlers and children's feet warm in cold weather and provide comfort on hot or rough surfaces.
Shoes also help toddlers and children maintain and gain traction, especially on slick surfaces, which can be beneficial for the toddlers developing balance and coordination and the shoes also help keep the toddler's feet clean which is important especially in daycare and other environments where hygiene is a concern.