The tire rule was implemented to help save the teams money. The tires were very soft and had a ton of grip, therefore wearing out quickly, hurting the quality of the racing, and rubbering up racetracks. Teams were bolting on fresh rubber every time the car hit the track.

There was an interview with Kenny Jacobs in Sprint car and Midget were he talked about it. He basically said the smaller teams couldn't compete because the WoO teams went out with 4 fresh tires every time they hit the track. I know this is the wing side but that's what I remember as the argument for spec tires.

With that being said I don't see why you can't have a spec tire from two manufacturers to help with cost.