Firstly, older moves are not dual type most likely because they did not think of doing that in the past, or the older games did not have the technical capacity to have too many unique moves with special conditions.
Next, although it's called a dual type move, from a technical standpoint it's a Fighting type move that's effective against different types to usual. In the same way Freeze-Dry is an Ice type move but is also super effective on Water.
Flying Press works well because the two types do not overlap. The types that Fighting is SE against, Flying is not. So there is no awkwardness with 4x damage against a single type. A Grass/Water dual type would make it 4x effective on both Ground and Rock which as the comment above says, would be devastating against Golem: 16x damage!
So in theory, they could add more moves in future that were considered dual types. But they would have to limit the damage to make it sensible.