I'm not an expert on the legal mechanisms but I believe it's a combination of all of those things through a hodgepodge of various local zoning regulations which the article references: limits on the number of unrelated people living in the same home where the limit varies by locality (i've always heard of these as anti-brothel regulations). Limits on number of leases in a single space or requirements for each leasable unit to have its own bathroom and/or kitchen. Requirements that each tenant have their own parking space. Lots of creative ways cooked up by local regulators across the vast USA to discourage anything but single-family homes occupied by single families.

Even what you described (single lease, 4 roommates) is very common and usually allowed but the single lease part is what self-limits the impact of boarding-house type places. You need to find 3 other people to go in on this place with. You need to trust those other people and coordinate lease payments and utility payments and deal with it when some of them to decide to move on. That's a headache!