Fans of Pokémon are familiar with the anime's rhythm by now: Ash strives towards a goal of winning a championship, enters with a strong team, and then when the time comes to move on to a new region, he starts over fresh, leaving that powerful team behind. It's a cycle that sometimes frustrates fans, but there's actually a very solid and respectable reason why Ash does this each time.
Ash's first real trip to a new region was when the anime began its Johto saga. In possession of the GS Ball which he was meant to take to Poké Ball expert Kurt, Ash meets Professor Elm and begins a new journey, questing after eight more gym badges. However, as he begins exploring Johto, Ash doesn't bank his entire old team with Professor Oak. Ash actually keeps his Charizard, now obedient to him, for the early episodes of the series.
In the second episode of Pokémon: Johto Journeys, entitled "The Double Trouble Header," Ash meets a young trainer named Casey who challenges him to a battle. She sends out a Pidgey, to which Ash responds by sending out Charizard. Pidgey is easily defeated, and she follows it up with a Rattata that she just caught, which is similarly defeated. Her final Pokémon, a Chikorita, is a bit stronger, but due to its type weakness is almost immediately taken out as well. Casey storms away upset at getting beaten so easily, and runs into Team Rocket, who convince her that Ash was cheating by using Charizard. Misty and Brock had voiced similar sentiments since Casey was clearly a new trainer. When Casey challenges Ash to a rematch, Misty and Brock actually cheer her on instead, offering advice as she battles his Pikachu. Team Rocket, of course, disrupts the fight to try to steal Pikachu, and joining together to defeat Team Rocket allows them to make peace.
Accusations of Cheating Weighed Heavily on Ash
Ash, particularly at this point in the anime, was often written as very childish, and stomping on a newbie with his overleveled Charizard is probably something that a lot of kids watching the episode could relate to. The episode's moral is obviously all about fair play, so having Ash do exactly the sort of thing real kids playing the game would do helps to get that idea across in an easily understood way. While Ash doesn't immediately send Charizard away after this episode, it's only about 16 episodes before Ash decides to leave Charizard in the Charicific Valley, both for training and to be with a female Charizard. Charizard is only used twice more before it leaves: once to help capture Chikorita, and then again when Ash goes up against the first Johto Gym Leader, Falkner. It seems that these accusations did end up getting Ash to change his tune and play more fairly; when Ash eventually headed off to Hoenn, he saw Gary leave his Pokémon behind to start fresh, and decided to do the same (aside from Pikachu) to avoid a repeat of his start in Johto.
This incident goes to show that Pokémon's Ash does have a good sense of fair play, and that bulldozing his way through a region with a team of developed Pokémon just wouldn't help him to accomplish his dream. Ash'll never improve that way, after all, so leaving his Pokémon behind is the right move, no matter how disappointing that fact may sometimes be.