Lol, because the Normal type exists for something... Going by that logic, the pure normal type Pokémon would have no need for a type. Let's say Tornadus was able to learn Roost, and then uses it (or any other temporarly pure Flying type pokémon). It becomes a pure Normal-type for that turn. But before gen V, they would become ???-type. They removed the ???-type in gen V, giving even more purpose of existance to the Normal type. One curious case is that of Togepi which is just Normal-type but when it evolves, it gains the Flying-type as a secondary type, mostly because, as a Togetic, it gains wings.
Imagine that there were these 3 types in the game at the same time: Flying, Wind & Bird. Consider the Bird type as a paralel to the Bug type which represents only pokémon based on those specific animals.
If these 3 types existed at the same time, the Normal/Flying birds, wouldn't be Normal/Flying anymore, they would be Bird/Flying. Doduo & Dodrio are even a better example to demonstrate this. They wouldn't be Normal/Flying, nor Bird/Flying, they would just be "Bird-type" (Despite Dodrio being able to learn Fly, we all know ostriches can't fly).
Other example would be Tornadus: it wouldn't be Bird-type, obviously. But it also wouldn't be just Flying. It would be Wind/Flying. Another that would be of the Wind type, but not Flying type would be Suicune because it is related to the North Winds; it would be Water/Wind.
This would apply to attacks too. Examples: Gust would be a Wind-type attack instead of Flying. Brave Bird would be a Bird-type attack instead of Flying. Fly would still be a Flying-type because it is related to the ability of Flying. In this hypothetical situation, the Flying-type would just represent the fact that the pokémon can fly.
Which is what it does to some pokémon actually. Thundurus & Landorus for example are real Flying-types just like Tornadus, yet they can't learn any Flying type attack by Level up and the only attack they learn by TM&HMs is none other than "Fly" (Thundurus can also learn Sky Drop, but that move is also related to the act of flying. Strangely, Landorus can't learn it, probably because it represents the land).
Of course, having these 3 types in the same game would be too stupid and it would cause conflicts with some bird-based pokémon. Some of them would have to be of 3 different types. Moltres for example (one of the birds I mentioned in the previous post) would have to be Fire, Bird AND Flying type. Some pokémon already suffer from the lack of triple types such as Reshiram & Zekrom. They can fly but since they already have 2 types each, and lack the Levitate ability (which remedies a bit the lack of triple typing), they are susceptible to Ground attacks.
Now, I am not suggesting they should make Pokémon have 3 types in the games. And returning to the Flying/Wind/Bird hypothetical situation, they named the type "Flying" to make a bridge between these 3 attributes. In other words, the Flying-type in the game covers pratically everything that:
1) it's a bird
2) can fly
3) directly represents the sky/wind. In this case, and speaking about Suicune again, since it can't fly, just because it represents the North winds, it is not enough to make it Water/Flying (which would also sound stupid). Tornadus, on the other hand, can fly and since there's only the Flying type in the games (for convenience), it is pure Flying.
One last thing about the Bird-type: It exists in the beta version of Red & Green. And Missingno., which a lot of people like to think it's a real pokémon, is Bird/Normal, but it is a glitch, so it's an unnecessary combination. Like I said, the Dodrio line would just have to be Bird type, not Normal/Bird. Again, for convenience, they changed it to "Flying". They couldn't apply the Bird type to a pokémon like Charizard. And if, for some reason, we still had the Bird-type instead of the Flying-type, Tornadus would now be a pure Bird-type lol...
I hope you all understand what I'm trying to explain here. I also used to think the Normal/Flying combo was pointless, but it has been some time since I came to the conclusion that it actually makes sense. I'm just sharing with you the logical explanation I tried to find to explain the reason for the Normal/Flying combo.