Addressing the bigger picture and not D3:
1) Well the money from the NCAA D1 basketball tournament is pretty significant (although D3 ain't seeing a ton of it). The TV contracts and level of competition are higher than NAIA.
2) The NCAA is made up of member schools who set the rules; the enforcement folks are then charged with enforcing them. The schools banded together and agreed on these rules to provide at least some semblance of a leveling playing field. Yes, the rules often seem strange, but these schools all voted on the rules and could at any time say "Letting a coach loan a player a car is okay". Then the screams will be that an Alabama coach loaned the star QB his car for a year (a car that the coach gets free from the local dealership). Or that the Alabama coach loaned the player a nicer car than the coach at Auburn loaned his player.
3) Someone has to enforce the rules that these members all agreed to abide by. What makes you think a different organization would make different rules? Let's say the NCAA ended tomorrow and all the current schools started a new organization. All the members stayed the same, what makes you think the rules would be different?
In theory all the California schools could break away so that the players can sign NIL rights. Would a league of just CA schools command the TV contract it has now? Based on TV ratings for PAC12 football, I am not sure. Now they might get other schools to join say the non-CA PAC12 schools. Some athletes might choose them over another school in hopes of getting NIL $$$. They would just play each other. Also, they would form a group to enforce rules and likely would have the same rule against coaches loaning a car to a player.
People seem to think the NCAA is some independent entity or a governmental agency that oversees collegiate sports.