Not like the Oak pokemon aren't training, all the ones that came back to the show came back improved, training with Infernape, Krokoodile, Snorlax, etc can help him get stronger that probably trainings against Charizard that are the same species.
Like Thriller I would like all of Satoshi to be at Oak, mainly because I like to see them all together when we get lab episodes(that hasn't happened since Hoenn) or possible cameo appearances.
That would solve many problems, but as said above, it just doesn't suit some of the pokemon's personalities. Charizard would want to keep training in the Valley, being with Charla, getting stronger (I know it could get stronger at the Lab, but it would just battle the same pokemon over and over, and would want a "Real" challenge in other charizards). Squirtle too, has the responsibilities of leading the Squirtle Squad.
The only ones I could ever see coming back from training is Gliscor, and to a lesser extent, Primeape. Gliscor was only allowed to go off with the Air Master to master Giga Impact and to train. By the time of the Sinnoh League, he returned, mastered Giga Impact, mastered several flying techniques and proved his strength to Ash and Paul. With that, I don't see any point in him returning to the Air Master, other than "Getting stronger". And as you said, it could grow stronger at the Lab, so with the exception of specialist training, I don't see the point. As for Primeape....Well it's both wishful thinking and the idea that it would actually retire as a boxer pokemon, and fight in actual pokemon battles.
Personally, I think they'll be some story of sorts at the end of the saga, where Ash will send Charizard back to the Valley, and Iris will say "What, are you crazy? That's your strongest pokemon, why are you such a kid and want to send it away?". Then, that could prompt Ash and Charizard to reassess their relationship, and perhaps question the idea of Charizard permenantely staying at the Charific Valley, permenantely staying at Oak's to be called upon, or to just try and split the two previous ideas.