>What public good could possibly come from such a restriction/ban?

Often it's to keep out the "wrong" sort -- don't want some uppity poor moving into your school district.

So small things like hanging your laundry to dry or hosting a lemonade stand will have the cops rolling up on your house.

(Yes, that's right -- I witnessed a township cop come destroy a child's lemonade stand signs, demand they disband, and threaten to cite the parents, and ultimately arrest the father within a week of living in an allegedly "upscale" neighborhood.)