Absolutely. I don't want him running muddy tracks through the house but he goes barefoot often. It's very common here in New Zealand.
We are a lot of the time a nudist family, so the children's bare feet do tend to get dirty as the day progresses, but more so in the summer when they are playing outside in the garden.
At the end of the day problem solved. Shower foot brush. Much cheaper then constantly buying kids sneakers from the shoe mafia when they get ruined. Children's shoes now cost more than they have in 70 years, the Footwear Distributors and Retailers of America (FDRA), a trade group that represents more than 500 companies, estimated in a letter to President Joseph Biden last week.