Besides, it wouldn't be fun to have Mewtwo in the party. It's a powerful psychic type and wouldn't be opposed to using said power to mess with the bad guys' heads. They'd either have to make it the weakest Mewtwo in the world or make it curbstomp nearly everything.
If Dragonite or even Gengar defeats it so Ash can catch it, how is it this uber powerful Pokemon. It can be ss strong as they need it to be, and yes technically it would be the weakest Mewtwo, hence why it would be captured if it is.
Honestly with the series as it is, we are unlikely to see it much anyway regardless if its always with Ash or mostly at the lab.
Plus if they were crazy enough to give it to Ash, it can always be a last resort. Using it against Elite Four / Champions / other powerful legendaries just used in instances to give Ash an edge, then start giving other trainers legendaries as well. Like Leon capturing Eternatus for example, since I can't imagine them giving it to Ash or Go.
Give Bea Marshadow or the dark type Urshifu for example. Or even Buzzwole/Pheromosa even though they aren't legendary.
Also allow trainers like Giovanni, Archie/Maxie powerful trainers that would give Ash trouble with his other non Dragonite/Mewtwo Pokemon and that would even give Mewtwo problems, like a Tyranitar being an issue or even Metagross.
I'm fine with a Mewtwo that isn't overpowered and is used in last roles or special moments, it doesn't need to be overused. So it can be like Palpitoad but shows up a bit more (once every 10 episodes or so) and the occasional legendary battle. Plus it could be used for training Ash's other Pokemon.
We saw the sheer difference between Leon and Ash with g-max Centiskorch along with Leon potentially catching Eternatus it would make nice for a good potential full battle.