Three Types:
Explanation: I picked the types that creates the least imbalance by process of elimination (or at least not to the point where one type becomes OP or is useless), avoiding removing types that require to remove too much types to be balanced (so no Fairy, Dragon or Electric removal), would constrain teambuilding too much (so no Steel or Water removal) or would remove important irreplacable tools (except SR, we'll get to it in a minute).
The end result is a combination similar to Tanny89k (no Teleport or U-turn), but notably keeps Knock Off around as a good progress making tool. Parting Shot can still be countered with Clear Amulet or Clear Body (which could be fun to use in a meta with good Intimidate users), or even Defiant/Competitive/Contrary on fast attackers (or, you know, not giving the move to everything).
Chilly Reception stills exist I guess.
- Probably the easiest type to remove without screwing the type chart much. Psychic has no defensive utility besides resisting itself and Fighting (already resisted by a ton of types), and so doesn't make anything broken by being removed, besides making Poison really good as a defensive type.
Calm Mind is the main notable loss (and I'm removing QD too), so special attackers will need to have more immediate power or setup with Nasty Plot or offensive setup moves.
- Other people have already explained it but yeah, Bug's really ass offensively and share the same resists as Flying (and Grass/Fighting is resisted by a lot of types already). The ground resist is nice but otherwise easy type to cut : at least it makes Grass types slightly better.
Rip Sticky Web.
And for the last type :
- My last choice was going to be either Rock or Ice.
Ice doesn't have any defensive utility and is mainly used while Rock's viability is dependent on having strong Flying, Fire and Normal types.
My first choice was Ice, to keep Stealth Rock around, but by doing so we empower too much types defensively by removing Ice coverage and splitting it across multiple types, with Dragon effectively having 1 weakness besides itself and coverage to hit Flying type being less common accross a lot of types.
Removing the Ice type would also remove Aurora Veil (and Screens) from the meta, and since Webs is already gone, I'd like to keep a bit of variety for offensive teams. With Rock (and Stealth Rock) gone, Flying types become really strong but are kept in check by Electric types and Steel types, and the strongest Flying moves either have recoil or are inaccurate (don't give Aeroblast on your subs pls, Flying-type Revelation Dance is cooler), so there's still built-in mechanisms to limit them. Fire types are a bit scarier but can still take damage from Spikes.
Big Winners :
: Only two weaknesses and one less type that resists it and no rocks to cripple them, so they don't have to use boots anymore. Having a ground immunity is also
: Same deal as Flying types : additionial resists can still be granted by abilities.
Other Winners :
: Really strong offensively and can check the Fires, kept in check by Grasses and bulky Waters
: Only one weakness.
: More important due to stronger Fire types (but has one less type to hit)
: Becomes the only type to both resist Flying and hit it for SE damage.
: More important to hit Flying types. Also has 1 less weakness and doesn't have to care about Rocks.
: Fairies are worse I guess. Steels are still good, and Ice types are sligthly better.
: Is better offensively with 2 resists removed and one weakness removed, still fears Flying-types.
: Better offensively.
Same position :
: Is more valuable due to Ground having only 2 resists, but is weak to the empowered Flying and Fire types.
: Loses 2 valuable resists, still good to check Flying types (and Poison/Ice)
Losers :
: Less useful defensively since U-turn is gone and slightly worse offensively with no Psychic, still decent vs Fighting and good to block Rapid Spin. However Dark types are less in demand, so maybe it can still get work done offensively
.
: Still good for checking Ghosts and strong Knock Offs but has almost no value defensively anymore. Lack of U-turn is still neat, and Fairy types being less valuable makes Fighting the only common type that can hit it effectively.
Big loser :
: Same as Ghost where no U-turn is slightly less useful. Fire types and Poison types are stronger in the meta, while Dark is weaker, and competes with Flying types as a Fighting resist. Still good as a secondary type for resisting Fighting and Dragon but not great anymore. Could be better in a meta with strong Dragon or Dark types.
Overall removing these 3 types changes a lot of dynamics without shaking the type chart too much, and losing types aren't fucked over too much (and/or can have stronger mons to compensate).