Well game manual says so, so....
The VG, fighting types have those combo hits, and grass types have those leech attacks, hence why Grass type in the TCG is the type that removes damage counters from itself. Lightning has paralysis and energy recycling, and psychic has attacks that cause the most different types of status conditions.
The TCG can't really add more types like the VG could. The TCG probably will fall apart if one more type was added, but the VG can have hundereds of types and still work. In the VG, you can use a team of 6 with 6 different types, but in the TCG, your deck will probably fail if you tried to play 6 types, well assuming you don't do Dragon or Colorless. In the VG, all you need is the game, and you have access to every single type of Pokemon, because it is hard coded into the game, so long as you catch them. In the TCG, you have to build a 60 card deck, and the pokemon use energy for attacks, and each attack has to use a specific energy. For the VG, there is no such thing as energy. You have 40 tackles, and you can use it whenever you want. Even so, you don't need to attach energy to it to use it like the TCG does, therefore you can have a team of pokemon from different types. In the TCG, because there is energy involved, you have to play one or two types.
The TCG will always have 600+ pokemon in the game, no matter what. The TCG can only have around 100 cards in a set, so adding more types means that there will be less of each type in the set. In the VG, you can capture whatever type you want, but in the TCG, you get whatever type is given to you in the 10 card booster packs. That is why more types is bad for the TCG, but makes no difference for the VG. The TCG is an adaptation of the VG, not a mimic of the VG. The TCG can never be like the VG.
Here is a new problem with the new fairy type. In the VG, you catch a fairy type, and you can use it whenever you want, however you want. In the TCG, you want to use a fairy card, but you can't, because you don't have the energy to use the attacks. This means you have to buy other products. A VG fairy can attack so long as you acquire that pokemon. A TCG fairy can't attack if you only have that card. You need energy to do so. It is hard to build a deck that contains more than 3 types, and if more types are added to the TCG, it is hard to find enough cards of one type to build a deck from, and this is especially true for the newest type. In the case of fairy, people who want to build fairy decks will probably hog all the energy that is released, that is buying theme decks and ETB's meaning that the fairy energy supply will be at an all time low. Even to this day, there is a pitiful amount of Metal energy in the market.
Pokemon TCG already diverged from the VG all the way since the TCG started. It is because of the energy cards. Because of Energy cards, you have to build a deck based on one or two types. In the VG is it more suitable to build a team of 6 where 2 of them don't have the same type. The TCG can never be like the VG. The only Pokemon about the Pokemon TCG is that they have Pokemon on the cards, and that's enough. The TCG is also has the flavor of the battle, but can never mimic the mechanics of the VG. I would also like each types to have its own gameplay identity, to add more spice to the game. Having each type do exactly the same thing would result in a monotonous game.