Laws like this are designed to keep undesirables out. Rich folks don't want 18 people living in a single house and attending schools in their district.

I think that statement is true for a lot of middle class people too.

Is there potentially an overlap between the kind of individuals that might want to live in a house with 18 other people and general criminality?

Mandatory low density zoning in general serves that purpose, yes.

If you need to own or rent a certain amount of land in order to attend the local school, then you can effectively keep out the poors (or even middle class, potentially).