The whole tire cutting thing, and RB stated it best, has to do with the the rubber folding over while in the turns.
Cutting the tires changes the slip angles that the tires work best at.
When I was running Mods' (pavement), we used the Hoosiers or Goodyears. It was ALL about the grip! Same deal with over powered and under tired. Ya gotta remember that these cars have a lot of horsepower, and weigh very little. Same with Legends Cars.
Different track surfaces, give different abuse to the tires (black top, cement, dirt). Cutting, or shaving the tires (in any form), will lower the effective use of the tire. Will it give better grip? Yes! But it will limit the amount of tire life (to some extent).
As I am going to run autocross; I will likely go with the slick type tire. It's a grip thing!
OldDawg has some very good info on tire cutting, as does The Tire Rack. (both good sites)
I think Megamang (Mike) has them listed in the reference material.
Tire rules will likely need to be brought up to INEX and 600 Racing. I don't want to get caught up in the politics of the rules. Not my thing! Would there be a better tire choice? .............. I can't say as of yet. Rules being what they are..... Ya have to make due with what the rules allow. It's the same whatever class, or type, of racing you do. At this point, cutting the tires seems to work for most.
Steve