My Dc went to a primary with a very relaxed atmosphere. No uniform, all staff and adults called by their first names (Lol I can't even remember the surname of the Head, only first name). It had what is known on MN as a very mixed intake, lots of social exclusion factors and children living in precarious circumstances.
The discipline was brilliant, based on empathy, kindness and respect. Great behaviour, bullying minimal and dealt with instantly and effectively. The children achieved really well, in absolute and VA terms.
I think this kind of learning and atmosphere is great. I could see them adopting a shoe-free policy.