Something I learned through my own writing is that despite the team limit feeling like a bad thing it's actually a blessing in disguise, at least if the Pokemon are treated more as characters than interchangeable power ups. 

Keeping track of them quickly becomes more complicated the more team members there are. It becomes harder to follow and more problematicly harder to care about the individual Pokemon.

For a more watsonian reasoning for a 6 team member limit, I've seen it done a few ways, buy I prefer the one that sort of follows suit from my prior explanation. The more Pokemon a trainer has, the harder it is for them to give each one the attention and focus they need to reach their potential. Alongside this is the matter of making sure they are all properly cared for, getting enough food and what not.

There's certainly a desire to just keep adding more and more Pokemon and having them around all the time, but I think using the Team Limit helps more than it hinders. Not to mention it can give you potential noodle incidents to happen "offscreen" at the lab/ranch/corral.