I think the reason that the APA has more players is mostly two fold...
First, good marketing...you can hardly find a bar or pool hall that doesn't have an APA league and fliers for it plastered all over ever wall, counter top and bathroom stall. Combine that with the fact that they've been around forever for word of mouth and league operators that do tend to actually try and recruit and you have market saturation.
Secondly, they tend to cater more towards the weaker players and social players. In other words...if you're just looking for a night out for drinking and fun, and don't want to have to worry about needing to get better to be able to be competitive...then the APA is the league for you. It caters more to the social players and we all know there are a heck of a lot more of them out there than there are the serious players.
This is not to say that there aren't some good players in the APA...and now with the Masters Division, this is probably more so. However, I think the better players still tend to drift more towards the BCA league system without the handicaps. We even tried to have an APA masters league around the area I play, but it folded after a couple of weeks due to the other teams quitting (I might also mention, I never saw any of my money back that I paid in to it either...it was just never heard from again)
Still, as a whole, you're not going to be able to assemble good strong teams in the regular division...and lets face it, once you get to a certain level, playing a match against the local drunk or bar fly really starts to lose it's appeal regardless of the handicap.
Although, now that I think about it, it is still probably more preferable than actually having to play on the same team as the aforementioned local drunk and barfly...