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The advantage of this is the ability to use the types as stats instead.
1) For Pokemon: Individual pokemon are not "Fire type" but rather have a "Fire stat", higher or lower as per the fieriness of the specific species.
2) For moves: Moves may have say 30 Fire damage, 40 Earth damage and a paralysis keyed to Air.
This generates a satisfying degree of enticing complexity while maintaining the inviting simplicity of 4 elements.