The solution is more Poison/Bug, Flying/Normal, Ground/Rock, and Fighting/Fire types, obviously.

You forgot Grass/Poison. May not be quite as prevalent anymore, but back in G1 there was only a single pure Grass-type.

And hey, how about Normal/Flying? That's another super-common one. Even now there's only a single Pokémon that's actually pure Flying-type, and it's a legendary.

In fact, when you get right down to it, Fire/Fighting isn't even all that common. There are only six Pokémon with that type combo—it just seems like a lot because all six of those are starter evolutions.

Further reading

You forgot Grass/Poison. May not be quite as prevalent anymore, but back in G1 there was only a single pure Grass-type.

 

And hey, how about Normal/Flying? That's another super-common one. Even now there's only a single Pokémon that's actually pure Flying-type, and it's a legendary.

 

In fact, when you get right down to it, Fire/Fighting isn't even all that common. There are only six Pokémon with that type combo—it just seems like a lot because all six of those are starter evolutions.

 

Further reading

But that's why I added Fire/Fighting, it's annoying if you want the fire starter in all of those generations.

And I did add Normal/Flying....

 

And I did add Normal/Flying....

 

D'oh! How did I miss that? I swear I double-checked your list multiple times...