Locally, for 1 season, there was a rule that you had to buy tires from the track. I get it. Problem was the track was not good about stocking the tires. They marked the tires with a rubber stamp. System had flaws. The track did demount/mount for free. There was no limit on sets of tires.
Before even trying to solve the tracking issue, I’d get them to accept the tire limit. ( I get you want all aspects worked out )
It does present some problems. Also are you going to make the rules state you need to use the same tires for qualifying as the main?
You could give an outline here and see what kind of pros and cons members here come up with.
First thought was If I am well funded I have several work arounds on the rule. I can afford several sets of wheels and tires for practice days. If I am not well funded I have to swap tires on wheels and/or have several sets of tires at once.
If it is not accepted, enforced or doesn’t solve a problem then why bother?
Well funded teams always have some advantages. I am not sure how you can mitigate that with a tire limit rule.