It's canon that Shinra doesn't have much of an airforce, or else the Tiny Bronco wouldn't be so big of a deal.
Shinra apparently has a bunch of attack helicopters though - both the ones you see regularly in game, and the weirdly high-tech ones you never see in use that are parked in Junon.
I think the Tiny Bronco thing really just was bad writing. It was just a rushed rational cooked up to justify putting Rufus and Shinra in rocket town, put Cid into the party, and give the party a new means of traveling to propel the story onwards.
From a narrative and logical perspective though, it makes absolutely no sense what so ever, so if they're gonna change anything in the remake, I hope they rewrite that entire section, or turn Tiny Bronco into a cargo air-plane, because seriously - it really is completely daft as it is.
EDIT :
I also hope they add roads, and a railroad system, check-points, other signs of civilization along the way throughout the world.
It just isn't believable at all that Junon and Midgar are completely cut off from each-other by mountains with no official method of traveling between them except capturing a chocobo, braving a swamp past the Midgar Zolom/Midgardsormen, crawling through a cave, and then walking across grasslands and forests with no proper places to stop and rest on the way.
How is Midgar even sustainable? Were are they getting their food? No proper farms nearby, no fishing villages etc. and no infrastructure for transport of food and other resources to the city from the outside at all.
How are they doing it? By an armada of Shinra choppers?
DOUBLE EDIT :
In fact, isn't the above point true for pretty much every town and major place of human residency throughout the world of FF7.
I mean Gold Saucer? How is that thing operational? You mean to tell me the poverty stricken people living in that town by that one cable cart are delivering groceries etc. once every week or so?
Where are these people getting that from?
What about the people of Calm, Nibelheim, Rocket Town, and Corel etc.? These places are all pretty much cut off from other parts of civilization yet they don't seem to have the stuff necessary to be self-sufficient. Are people living in FF7 all hunters and gatherers? If so, shouldn't there be warriors walking about everywhere? I mean, the FF7 country-side isn't really all that hospitable after all, with all the dinosaurs, weird hybrid monsters and killer robots on the loose and whatnot.
I mean, rocket town doesn't even have a wall to keep that stuff out.
This even impacts the plot. I mean, Cloud, Sephiroth and Zack arrived in Nibelheim in a truck -
in a truck - but hey, guess what? There are no roads leading to Nibelheim. It's also past several mountain ranges and rivers that apparently, can only be crossed on foot, and with a sand-buggy, chocobo or boat.
How did Rufus and Co. get to Rocket Town if not via helicopter, and if the helicopter can fly that far, why do they need the Tiny Bronco?
How did they move Sister Ray all the way to Midgar without proper infrastructure for travel? The armada of choppers again?
How did Shinra move an army to Wutai? They all rode across the swamp on chocobos, crawled through the cave, walked to Junon and caught a boat, then walked again? Or did they just fly there directly? Why does Rufus need the Tiny Bronco again?
WTF GOD DAMN IT, FF7 IS RUINED FOR ME NOW!!1!!!!111!
j/k
Seriously though. Remake. Fix the god damn infrastructure of the world.