This is an important distinction. Humans evolved in tribes, and many of our instinctual responses to how we think we should work together are optimized for such a setting. But these things just can't scale upwards. There are many things that work well at a community level that fall apart with larger groups. So when we see a problem in the world and feel our heart-strings tugged, we should be suspicious that our emotional response is something that can really make sense in the big picture.
I do agree that such things might be able to work at small scales. But I suspect that the threshold is well below the size that you're citing here.
Markets work because they are irrational, and move with people as situations change - like a subconscious reflex - planned economies require conscious effort to reapportion their efforts in the face of change.
The solution to socialism is collectives - lots of little ones from 50-500 people, which then interact with each other using market settlement and price adjustment mechanisms.
I'm not a proponent of anything Authoritarian, but communism on a small scale does fascinate me.