Yes, in practice, it works the same, but the use of Primary type and Secondary type is to indicate the main or more prominent/recognizable type of that pokémon. I also think that's very important. In fact, I think some pokémon should have their Primary and Secondary type switched.
About Noibat, I've wrote once in this forum about how I belive Noibat was not meant to be a Dragon-type, and instead a pure Flying that would gain the Dragon-type upon evolving into Noivern. Hence why Noivern is Flying/Dragon instead of the usual Dragon/Flying. You could argue that some pokémon have the same type combination with only the order reversed (e.g.: Golem and Rhyperior) but, even though I also don't think Flying should be used as some kind of sub-type, the truth is, it is (at least in GF's mind).
I'll just leave the link to my post about Noibat:
Post
Now, there are only two cases (correct me if I'm wrong) where the Primary type is changed instead of the secondary type.
Onix -> Steelix
Swablu -> Altaria
Onix was probably unavoidable as Steelix was introduced a gen later, but Swablu and Altaria could have had Flying as their primary type instead of Normal and Dragon, as there is a type change occurring.
If you notice, they try to avoid this as much as possible. Take Skorupi for example. The only pokémon with Secondary Bug-type are Anorith & Armaldo (Fossil pokémon, which have the tradition of using Rock as the primary type - Carracosta's line being the exception, but that's a mystery for another post) and Skorupi itself. Why isn't Skorupi a Bug/Poison like all other Bug/Poison pokémon? Because there's a type change. Skorupi loses its Bug-type when evolving into Drapion which is Poison/Dark.
Skrelp is a similar case. A pokémon which lives exclusively on water, but is Poison/Water, not Water/Poison, again because it changes from Poison/Water to Poison/Dragon, when evolving. Why couldn't Skrelp be Water/Poison and Dragalge be Dragon/Poison? It seems GF doesn't like changing the Primary-type, that's why.
Back to Altaria, one of the reasons they weren't primary Flying is because only recently GF started to care more about the Flying-type, introducing Tornadus and such. It would make more sense as Altaria only has a Dragon-type because of its Peng origin, which is pretty unnoticeable in its design and I don't think that qualifies as a reason to have Dragon as primary-type. Also, wouldn't it make more sense for Rayquaza to be Flying/Dragon, as it is the Sky representative of the Weather trio? (Rayquza is a pretty good example of an actual dragon, though, so I'd probably leave it they way it is.)
But even now, they changed Altaria from Dragon/Flying to Dragon/Fairy in its Mega form. Had it been primary Flying, we now would have a Mega which changes the Primary-type, or maybe not as they could very well ditch the Dragon-type to avoid that... But GF likes hype, so a Fairy/Dragon would always sound cooler than a Flying/Fairy.
And let's not counting the amount of pokémon that can clearly fly but are not Flying-type. What's interesting is most of those pokémon are usually part-Dragon or part-Bug, so they always leave the Flying-type out in favor or another type when pairing with those 2 types.
All this leads to what Mitja proposed the other day about an airbone mechanic which I also believe could solve a lot of these oddities.
