This was originally done on the GameBoy because it was very limited in hardware. They used static sprites and just animated moves, Pokemon Stadium was made for the purpose of showing what these Pokemon are actually doing without the limitations of the gameboy.
Since Gen 3, Pokemon has always been behind in capabilities.
>Gen 3
no animated sprites, until Emerald which look terrible
>Gen 4
despite the GBA having games like M&L: SS, they are STILL using static sprites
>Gen 5
finally using animation, but they aren't actually attacking each other, instead they are mainly still animating the moves despite the DS being able to handle it fine.

This has been an issue for a long time, but it has only gotten worse over the years. Fuck, now they can't even properly scale the models.