Ultimately for a lot of people the problem is foundations. It just happens to be that both sidedness and long string length is what forms that. You get poor styles when people rush into big concepts too soon, or into moves they don't have the grounding for. I think the problem usually originates in the very beginning of taking up the sport. If you have people giving you shit about hitting -every- move both sides, their legs are naturally going to become much more ambidextrous. Further, if they have people making sure they can hit the move over and over consecutively (on both sides, if the move calls for it), then you'll have a player with strong links and good contact length. I would say that once you have a strong foundation as a -guiltless- player, THEN move into what you want to do with your game. Learn all of the core concepts, and sets (tiltless, BOP, double downs, spinning, ducking, whirl, drifter, swirl, symposium, dlo, eggbeater, atomic, stepping, pixie, quantum, fairy, etc.), then start fleshing out how you want to play. It will take longer, but it will be much more rewarding. Just because you can hit a move doesn't mean you should on a regular basis. For example, if you can hit PS Whirl, and start hitting it at the beginning of every string and whenever you can, but can't for the life of you hit a flipside PS Whirl, you'll end up with a REALLY good strong PS Whirl that you can hit into and out of whatever you want... except PS Whirl.

Further, playing like this can have other ramifications. For example, when I first learned drifter, I REALLY had to work at it on my flipside because of how I naturally leaned over the bag, due to being sideways right. Eventually flipside drifter became much stronger, and now I own it. Consequentially, I feel that in all of my moves, I'm a little more centered. It's not so black and white as being able to hit certain concepts.
Of course, people will say, "But it's freestyle!!! Play how you want!" Whatever.

I fell in love with footbag freestyle, not hacky sack. To me hitting big moves on one side is as bad as hacky sack.
Oh, and session highlights:
(~ 1 1/2 hour long session)
I did a lot of work on stepping each side, and worked the other concepts that I'm solidifying. All of the concepts I'm working on right now really seem to be coming together, and I'm feeling like I can make strong links between all of them. No real mind-blowing strings stood out today.
Peace,