What Game is perfect? Old Nine-Ball Honest Effort? Push-Out Nine-Ball, Texas Express Nine-Ball, Call only the 8 Eight-Ball? Call everything Eight-Ball? Ten-Ball World Standardized Rules? Ten-Ball with Nine-Ball rules? 14.1 Straight Pool? Bank Pool? Pool300? Bonus Ball? 6Pocket? One-Pocket? Should I continue with this? A marketing manager would not even know where to begin.
This is like saying cards have a problem because you can play Gin, Cribbage, Bridge, Euchre, pitch, blackjack, etc., etc. However, that is exactly what makes a deck of cards (and a pool table) so perfect. They are both remarkably flexible
game platforms where you can play an almost infinite number of games.
14.1 is pretty damn good. From your point of view, I think the only downside is that one player could run 150 and out. However, the player's you frequently reference -- the ones that can't play rotation games -- would never run 100+ balls. The game is hard, but that doesn't mean it has a "flaw."
No game or activity is worth doing if it's easy. You want to attract new players? Let 'em play APA 8-ball. Court the higher-skill levels to get into 9-ball or 14.1, start other non-APA leagues for people to "graduate" to. When people's handicaps go up, reward them with something... free/discounted table time, for example. Let 'em learn how to pocket balls and get shape by playing offense-only games like Pool 300.
I mentioned it before, there's a book called "300 ways to play billiards". Have you read it to see what's in there? Maybe there's already a game that meets your desires?
Edited to add: Any newcomer to the game is going to have difficulty getting the cue ball and object balls to do what he/she wants them to do. Because of that, I think the rules of the game being played are largely irrelevant.