I generally agree with you on the point that a "good Pokémon team" can be better encapsulated by other attributes, including those you mentioned. I would disagree on assumptions being very wrong, because I am not assuming that the objective and constraints chosen are ideal or even good enough, I am choosing them simple for illustration purposes.
I actually found it interesting that in spite of what is a clearly overly simple model, the non-legendary non-multi-starter you eventually get is quite a good one, in my opinion better than what the naive constraints would lead me to think.
Also, keep in mind that I'm not talking about competitive matches here, just mainline gaming. For that end, types are usually all you need, and in that area the main thing I would do is generalize type constraints to not be just defensive but also ensure each resistant Pokémon has a good enough attack against that type.
In my opinion, abilities, nature, objects are:
1. Too complex for such models (MIPs are still exponential-time)
2. Overkill strategy when all you wanna do is beat the league
That's where I disagree as well, the non-legendary non-multi-starter is also a crappy team as Pokémon isn't a rock paper scissor game since a long time.
You'd need to take into account innate abilities, how to also understand the impact of HP/ATK/etc in each Pokémon.
Snorlax for example is quite good, as it's pretty tanky and have a good moveset that can help it set it up.
Dragonite has multiscale, stuff that doesn't show up in by just looking at Pokémon types and stats.
Again, my main point was... analysis could be much more interesting if it analyzed battle data, rather than a very shallow assumption that a combination of Pokémon types and stats can win a battle.
I actually found it interesting that in spite of what is a clearly overly simple model, the non-legendary non-multi-starter you eventually get is quite a good one, in my opinion better than what the naive constraints would lead me to think.
Also, keep in mind that I'm not talking about competitive matches here, just mainline gaming. For that end, types are usually all you need, and in that area the main thing I would do is generalize type constraints to not be just defensive but also ensure each resistant Pokémon has a good enough attack against that type.
In my opinion, abilities, nature, objects are: 1. Too complex for such models (MIPs are still exponential-time) 2. Overkill strategy when all you wanna do is beat the league
But that last part is just my opinion.