These weapons were probably too complex to be produced cheaply enough and in large enough numbers to become a standard issue weapon, as well as being too complex to be maintained in the field.
In the early to mid-1800's, annual income for an average worker was something like $400 - $600. A muzzle-loading rifle cost roughly $150. The rifle cost 1/4 to 1/3 of an average persons annual salary...
Also, almost every single gun was individually created. No real standardization of parts. That didn't really happen much until the mid-1800's. Even as late as the civil war, just providing ammunition was a hassle because the weapons weren't standardized enough.
Prior to that, the gunsmith hand-made his gun barrel, and then hand-made the gun around that. When it was finished, he hand-made a mold for the bullets for that individual rifle. Nowadays, we have muzzle=loading rifles in standard .32, .44, .45, .50, .54, etc. We use standard 44, .49, .53 balls, etc...
Back then my rifle might have used a .525 ball, while your "identical" rifle made by the same smith might need a .510 ball.
Really, as interesting as it was/is, the "air" rifle never went anywhere... It's still considered a "toy". I've been looking, and haven't found any real data on the Lewis and Clark rifle. What kind of FPS did it produce? How did it vary after several shots? The guy in the video really doesn't give any factual information regarding accuracy or velocity. Breaking through a 1" board at 100yds doesn't mean all that much, IMO.
For accuracy, the rifle would rely on a
tight fit in the rifling, and that was known at the time.
In every other rifle at the time, that was achieved with a tight-fitting patch/ball combination. No bullets (or very few anyway) were being loaded from the breach, and none were contained in cartridges. That means several things... For one, all muzzle-loaded balls were "
undersized", so would simply roll out of the barrel if the gun was tipped (the patch prevented that). But with breech-loaded projectiles the ball/bullet is
over-sized, so gets "slammed" into the rear of the rifling (engaging the rifling and sealing the bore).
The air rifle would have needed the latter... And if it used over-sized balls it would have required substantial pressure to form the ball to the rifling and seal the bore. Without doing that, accuracy would suffer greatly, as would velocity. For a repeater, that would have also meant wasted energy as compressed air passed around the ball as it traveled (bounced?) down the bore. Modern air-rifles get best accuracy with skirted pellets that flare open from the rear to engage the rifling and seal the bore. Those type of projectiles weren't used until the civil war (half a life-time after Lewis and Clark).
Honestly, it's a cool gun. But I think it's being over-hyped. It never went anywhere, and never saw much use/popularity beyond that of a toy. My guess is that one big reason is that compressed air simply isn't as easy and efficient as a mixture of sulfur, charcoal, and potassium nitrate. That's also why it isn't replacing gasoline as a fuel, even though it can be used to turn over a motor.
It had usefulness as "show" with the native people L and C came across, but I doubt anyone would have been rushing for that weapon over a standard black powder weapon (or a knife) had a battle come up. L and C took a small cannon for the same reason (show). Keep in mind, the first powder-operated firearms used in battle were mostly for "show" as well!