These are all reasonable and logical arguments to be against an Air Rifle, and I suspect you won't like my response.
Rule of Cool is King.
The bold face is also included. This means that the physics of the game world will overlook IRL flaws if the result conforms to the subjective definition of "cool".
The ability to compress air for propulsion of shot is wildly inefficient when compared to gunpowder.
IRL, yes. I agree. But mechanical legs are inefficient compared to wheels or treads, and Mecha are a staple of medium Sci fi. I believe rule of Cool will override this and allow Air Rifles a niche much like how Tanks and Mecha can have their own complementary niches.
Its projection mechanism is vulnerable.
The gun itself is a hand grenade waiting to go off considering it needs to hold pressures of around 60,000 PSI if it wants to contend with a normal rifle's ability to kill, even just 40,000 if we want to be in the pistol range. Thats just waiting for it to explode the moment a piece of shrapnel hits it and I'm pretty sure "Its made out of a super strong alloy" won't fly with MoP without adding even more expense to the rifle.
I assume these points are related, so I'll address them together. Damage to the air propulsion could be catastrophic, yes, but I imagine the wielder of a firearm will have just as bad a time if a traditional magazine cooks off. Perhaps it is more likely, but Rule of Cool will mute it. Conversely, there is no build-up of carbon in the working parts of the weapon, so routine maintenance may in fact be easier.
Its way of reloading adds too many moving parts a soldier needs to keep track of.
You have two things to keep track of. Magazines and a Gas Canisters. I realise our grunts will be eating the period-equivalent to crayons, but this cannot be beyond them.
It doesn't scale well without needing to stretch reality even further than we already are.
Not a fan of compressed air powered Artillery guns? That does stretch my disbelief a little too much, but I'm sure we could make something work.
Not to mention its based on an artisinal weapon, and the fact that 200+ years since its creation IRL we still haven't figured out a way to compress air to the point to make such a weapon viable because its not, all that stretching reality does is force us to spend time and difficulty rolls adding more and more to each design to make them workable.
Firearms used to be artisinal too. With some help from Rule of Cool, we can pull it off. After all, how much actual effort was put in over that 200 years? Probably less than we could of, because in this universe firearms performed better. If people genuinely believed air rifles were better, they would've put the effort in.
Also, no children- when you scale up an air rifle to fire pellets that can kill someone they very much are not silent anymore. Because the sound a gun makes comes from the gas pressure leaving the barrel, and once you pass 500 psi then you start to create sonic cracks like a rifle.
The silent weapon assertion is pure Rule of Cool. You are right that any expanding gas makes noise, regardless of whether it is caused by compressed air or an explosion. But having a weapon with an integral suppressor because of how it works is, imo, Cool.
I'm expecting the Air Rifle to have both strengths and weaknesses compared to a Firearm. A firarm may have higher effective range and stopping power, whilst an Air Rifle may be more easily supplied and allow for close-range engagements without revealing their position.
I think an Air Rifle is Cool. And I don't think you do. But in a game like this, we are constantly going to get proposed non-IRL appropriate weapons because Cool. We were gonna have this friction sooner or later. Where do you draw the line on "Cool but Impractical", when the setting let's us ignore the second part?