I used to do it back in Smash 4, when there was no overlap in the types of Pokemon. But once Trainer came back and they added Inceneroar in Ultimate(giving us multiple Fire, Water and Dark types), I gave up on it.
That said, we're only missing 6 types. You could cover that with 3 Pokemon.
Normal
Fighting
Flying
Poison
Ground
Rock
Bug
Ghost
Steel
Fire
Water
Grass
Electric
Psychic
Ice
Dragon
Dark
Fairy
Let's see...Garchomp/Kleavor/Froslass. Or Baxcalibur/Golurk/Kleavor.
I keep my team from each game. So...Gen 3 to Gen 9...plus my Dark team...like 80ish of them?