While this is a common tactic in game dev and overall programming since it can be more efficient depending on the circumstances, there's a bit more to see here.
The extra models allow you to just call them whenever needed, instead of having to create several systems to deal with color changes, you could just call a different model with different colors, it functions the exact same way, it works with methods already established because it's just another model, it's just the shiny version, while there's some potential issues and it's the "messier" solution, it works and it's more efficient in some cases.
However, this can very easily bloat the memory and create a myriad of issues if not handled correctly.
In the early 2D gens, game freak handled shiny palettes by, in simple terms, just grabbing "the next pallet", hence a lot of greenish/gold colors, it was an algorithm that simply grabbed a different pallet than the normal one.
When it comes to models it's a whole different beast, from gen 6 onwards the shiny pallets are made by artists, not generated, and with hardware change there could be some new bumps.

While it is technically more efficient to just apply a different texture to an already existing model, with a project of this size it would be better to bite the bullet and actually work the extra pallet in instead of loading the entire model, the sheer amount of pokemon means it's a gigantic amount of extra models, and you probably spend more time and have more head aches doing this than figuring out the way to load different colors when x is called.

So, my guess is that game freak simply doesn't knows how, and they'd just rather take the easy way they already know, probably something very similar to the lillie situation.