Quite frankly, if centers were smart they would all do pre-pay only.
Sure if you don't do pre-pay, then there is the possibility that the bowlers will bowl more games and consequently generate more revenue. Unless of course they choose to walk-out, in which case the center takes a loss.
As someone said earlier, when was the last time you got to golf the course first, then pay? Have you ever been able to hit balls at the range BEFORE paying? How about hitting balls at the batting cage? Riding go-carts? Putt-Putt? Do GameWorks or Dave & Busters let you play first, then pay? Better yet, when was the last time you walked into a bar and told them you'd pay AFTER you were done with your drinking for the night?
It might be a bit inconvenient (note sarcasm) for you to make that LONG walk back to the counter to say "can I add a few games?," but I think it's much more inconvenient for the center to say "hey, where'd that guy/group on lane 12 go? That was 16 games at $3.00 out the door!"