I think that until you have a 160 average, you should only be allowed to have one ball: plastic with a pancake core. Bowlers with averages like that only really care about how the ball looks anyway, and there are plastic balls in virtually every color you could want. They're not good enough to hook anything, so they should be required to get it drilled with a conventional grip.
Once they get over a 160 average, they can purchase an entry-level urethane ball, with a puck or pancake core (like the PG or Scout). They can get it drilled fingertip, but it has to have a label drill on it. They are not knowledgeable enough to make effective use of a weight hole or understand what effect it has on ball reaction. They need to learn to control their hook, and urethane will do just that.
When they can average 180 with that ball and average at least one clean game in a 3-game set, then they can purchase a mid-priced reactive ball. No particles, and it can't have lower than an 800-grit finish on it. Such a bowler is too ignorant of oil patterns and such to not understand why a 400-grit high-load particle ball is not hooking, and those bowlers really only care about seeing big backend reaction anyway. Letting them purchase a particle ball will only confuse them with its smooth, controlled reaction. They cannot, however, have more than one ball, so that urethane ball they used before must be traded in (like a core charge, no pun intended). They wouldn't understand how to choose balls to suit lane conditions anyway, so having multiple balls in an "arsenal" is silly.
Now, once they pass 200, more options open up. They should have their choice of particle balls, but no asymmetrics. Asymmetrics are very sensitive to release changes (mistakes), and that kind of bowler isn't capable of being consistent enough to effectively use an asymmetric ball. They are allowed to own three balls, but one of them has to be a plastic spare ball. They need a plastic ball because they aren't good enough to just flatten their release for spares.
And finally, if you average 225 or higher, you have your choice of balls. Asymmetrics, symmetrics, high performance, entry-level, pearl, solid, particle, reactive, whatever. These people are the bowling elite, they truly understand equipment choices, lane conditions, releases, lines, the whole shebang.
Of course, this would require a lot of work and sacrifice on the part of pro shops. It would, however, make it clear who the true elite players are and it would give those elite players a sense of being better than everyone else because they are allowed to have more, better equipment. They would no longer have to put up with the ignorant masses who feel like just because they carry four six-ball bags to league every week, they're great bowlers. Outsiders wouldn't mistake such a person for a good bowler because only the good bowlers would have so much equipment. You could just look at a player's equipment and know if he's a good bowler or a low-life beginner.
SH