Mewtwo had his own little kingdom there, and if that was ever introduced into the game it would be awesome because to date he's the only Pokemon, legendary or otherwise, to do such a thing. He even posed as a Pokemon trainer! How cool is that?
I mean, he was a Pokémon trainer, that is a functional category relating to his role in a battle. Hence, he does battle other trainers, and defeats their Pokémon. As he said, "The world's greatest Pokémon master is also the most powerful Pokémon on Earth," which ultimately makes sense anyway, because mostly trainers just rely on their Pokémon and pander to them while taking credit for their actions. As a result, most of them are reducible to actions or traits which are interchangeable. He is the apotheosis of this order, but critical of it, and his interests and desires despised to illogical lengths. The rest of the anime is carried out in the shadow of pretending that their battles are important while knowing that Mewtwo was actually better than any of them. And they don't do much else. You figure it might be best not to do the same to the games, or lift that coterie out of context.
In any case the humour of lines such as, "Like most Pokémon trainers, l too began with Charmander, Squirtle and Bulbasaur," especially when used against a bunch of people including Ash Ketchum, might be a bit subtle and seem out-of-place in the current games, if they're similar to the last few ones.
or fantasizes about movie!Nurse Joy, or something. XD
Eh, there are plenty of girls, if that were the question, any particular reason why you would select that one? In any case, you presume that a powerful Psychic could do a fair bit, but anyway, maybe that's why it's a Psychic Pokémon. I'm pretty sure that their actual relation to such was fairly staid, but maybe you mean that you ended the game on encountering Brock...? He was at least slightly ironic about it, with a Geodude and Onix sent out as Pokémon.
Otherwise you might have the wrong culprit in mind.
Just for kicks I posted a youtube video for Leafgreen of Mew vs Mewtwo. I think I have too much free time on my hands to make my own pokemon battle scene similar to Pokemon Movie 1
Did you find a guy named 'Ash' or such and turn them to stone?
The excitement is at its limit here, and once you enter that battle and see a wild Pokemon at level 70 you're like "OH SHOOT!!!" and proceed to get your butt kicked.
I'm not sure if players, having beaten the E4, were supposed to be surprised by one wild Pokemon, after they already have the Master Ball and might not have gotten rid of it, being levelled a few 10-15 levels above the E4's trainers. If that was by then a difficulty, they could have just used it. They don't have a reputation for that, in-game, where that needn't be the point - unless they're being used.
Mewtwo definitely needs an in-game story behind it, but I don't want it taking over the spotlight a la Gen III cover-Legends. Despite the fandom and the officials treat and regard Mewtwo as a Legendary, I personally don't see Mewtwo as a (genuine) Legendary Pokémon, because it's a manmade Pokémon.
Well, an unintentional man-made Pokémon, made from another 'legendary,' who is then generally held to in some way have dissociated itself from this quite strongly, but that doesn't seem relevant to the qualification. Are you presuming a bit much about the term 'legendary,' here, which generally responds to what a Pokémon is (otherwise nobody cares) rather than to incidental questions which don't determine its being? It's not like all other legendaries were formed in the cavern of legendaries, either.
There's generally an element of human classification in the term 'legendary,' though, which is why Gastly for instance need not have been considered such, so in that sense Mewtwo has a better claim to the term than most. Is it that out of consideration that humans could create, if indirectly, a Pokémon of significance to the Pokémon universe? In that case, their relation to such would ultimately be decisive, not their relation to humans. Its status as a Psychic type should be enough to show that its human relations are part of what make it special, that is different from an 'ordinary' Pokémon, and should not be allowed to be to its detriment.
Other than that, though, Mewtwo generally seems to function better without being involved in some in-game drama, as this is part of its mystery and sense of detachment. It hence becomes a purpose for the game, rather than merely an object for it. It has a general relevance to the world before this, while later legendaries are increasingly props playing a part in this, and hence become accessible, possibly multiple times.