Couple other things to consider:
1.) Fire/Water/Grass works amazingly well because each of those types resists the type that it is offensively strong against, and each type is also resistant to itself. I'm not aware of any other triangles that function quite so perfectly.'
2.) Fire/Water/Grass also have no immunities. When you look at Fighting/Psychic/Dark, Dark has a big advantage because it is immune to Psychic. Water/Ground/Electric is the same. Any triangle with Steel also has a sizable unbalance because Steel resists a ton of other types including Normal, which puts them at a sizable defensive advantage.
There's a reason I guess why Fire/Water/Grass has persisted for so many games. It's a very rigorously balanced triangle.