That is actually quite interesting. Especially the part about the monsters being bound to the trainer's soul, and there being a natural limit on how many a person can carry around with them at once. It would certainly explain why everywhere you go there's people who for whatever reason don't have 6 monsters with them, I mean even the gym leaders in the games never have 6. I don't think the original elite 4 did either.

And I guess you are right. Tournaments in a world like this would make sense, but I imagine trainers would still be expected to do something of actual practical use from time to time.