I think the regulations on corporations (jklann’s point c) is to eliminate a conflict of interests. Imagine a clothing manufacturer, food vendor, or other related company owning a NFL team. Suddenly that team is getting favors, price breaks, and amenities while other teams are getting late shipments, extra fees, wrong products, etc. It could also be possible for a large company to funnel revenue into it’s team without the league’s consent (accountants can be very creative).
Non-profit organizations get numerous tax breaks so that could schewer the revenue sharing in their favor, as Nametag mentioned.