Not to rain on your parade or anything, personally I wish I could set fire to the rain.
Uh... I think the Lylatians are a little more advanced than what you have credited them for O.o.
The fighters they use are capable for both aerial and space warfare on a dime (meaning no change).
All fighter jets on the lylatian side don't exactly need wings to fly, but more so to stabilize for planet warfare.
They use the jets on the wing boom jets (The large triangular structures on the arwings, wolfens, and basic cornerian jets) to do the actual turning and maneuvers in a near zero-turn style way. Which means the elevators on the tail fins are pretty much out of date. Though they still remain on the wings, it's mostly for remaining stable and quick turning on air resistance.
The bombs might not be missiles, but they are mini nukes that home in or just drop and explode. A charged shot will also effectively become a missile it's self and home in.
The planes are also able to withstand an ungoddly temperature (Hence the journey to solar without a complete meltdown or overheating), go into a black hole (worm hole, not a real singularity) safely (with the help of G-Diffusers. Proven in comics, and even do able in game.), and deflect any projectiles with a magnetic pulse when spinning. There are even varients to all the fighters according to Command and SNES SFII.
Shoot the Arwing II had the ability to transform into bipedal machines, or go underwater without ripping apart.
There is also a weird giant satellite diffusing laser gun thing orbiting Corneria that can shoot... pretty much anywhere in the lylat system, and destroy an entire armada. Not sure if it's still operational... because there are hundreds of alternate stories in Starfox.
Really, the only things the fighters suck at is the armor, and speed. The arwings pretty much real over after a direct file from a small plasma round, and direct contact to any surface pretty much devastates the thing. The cornerian ships can go fast, but they are harder to control. To turn, they must roll 90, then turn when going faster than cruise apparently.
Oh and flying barrel rolling tanks.