Well if they were to do this now they would use
the current Type organizing:
GRASS
:
Grass &
Bug
FIRE :
Fire
WATER :
Water &
Ice
LIGHTNING :
Electric
FIGHTING :
Fighting,
Rock &
Ground
PSYCHIC :
Psychic,
Ghost &
Fairy
COLORLESS :
Normal &
Flying
DARKNESS :
Dark &
Poison
METAL :
Steel
DRAGON :
Dragon
Though I don't know how well this would work if tried to put into the game mechanics.
Volt-Ikazuchi brings up the point that, in the TCG, Type interaction work differently as it's case situational rather then having a rigid structure. Infact what Type the Pokemon is doesn't directly determine what its Weak or Resistant to, it's only referential on the card makers part. The Pokemon's Weakness and Resistance are the ones which would make the "most sense" under the TCG's limited Typing, and even then that would sometimes cause quirks where a Pokemon which wouldn't normally be super effective or resisted in the games is in the TCG for specific card interactions. Like, if we were to consider Weaknesses and Resistances the TCG Type Chart would look something like this:
Side Column = Attacker
Top Row = Defender
W = Weakness
R = Resist
Im = Immune
Orange = Conflicting Results
| | | | | | | | | | |
| R | R | W/R | - | W/R | R | R | R | R | R |
| W | R | W/R | - | R | - | - | - | W | R |
| W/R | W/R | R | - | W | - | W | - | R | W/R |
| R | - | W | R | Im | - | W | - | - | R |
| R | W | W/R | W | R | R/Im | W/R/Im | W/R | W/R | - |
| - | R | - | - | W | W/R | Im | W/R/Im | R | W |
| W | - | - | R | W/R | Im | - | - | R | - |
| W/R | R | - | - | R | W/R | - | R | Im | - |
| - | R | W/R | R | W | W | - | - | R | - |
| - | - | - | - | - | Im | - | - | R | W |
I think that's correct, though even if there's some mistakes, you can see the issue via all the oranges. Also, since Types were categorized via "flavor" than balance (at least in the sense of a rigid system), we get other issues/oddities like Grass & Darkness being SUPER BAD offensively and Fire being really good defensively (Steel is also good defensively but that's normal).
Also, in general, I feel a lot of Pokemon would lose some identity.
I think it's best to let sleeping dogs lie. The TCG Types work off a system that works for them but not compatible with the games. That said, even though mechanically there's no place for them, I can see the games incorporating the TCG Types thematically. Like maybe in one game have the Gym Leaders (or equivalents) expertise reflect the TCG Types (Elite Four would be more specialize types; Champion would be a coin toss). Or maybe just has a special group of 10 Trainers representing the TCG Types which use any Pokemon associated with their TCG Type.