The paper cutter Sharps can be, and usually is, used that way. I don't know about the Smith Carbine. If it relies on the brass case to seal the breech, you're going to have a lot of blowback if the case is not used, which may or may not be a problem, after all, revolvers have a lot of breech leakage around the cylinder gap.
The metallic cartridge was invented for a reason. Paper cartridges could be loaded fast but they relied on the gun's breech mechanism to seal the breech, usually imperfectly. Brass cases on the other hand expanded with pressure and acted as a seal as well as containing the charge. They sealed the chamber under pressure sort of the way a tubeless tire seats and seals on the rim when you inflate it.
Once percussion ignition was developed, it was only a very short time before they found ways to incorporate the percussion cap into a brass or copper cartridge.
The percussion muzzle loader was indeed a very short lived era in the history of gun development. If I remember correctly, percussion ignition came about around 1836 or so, ending hundreds of years of the dominance of the flintlock, but only around 25 or 30 years later, the percussion muzzle loader was rendered obsolete also.
And here we are in the year 2016 and nearly all modern rifles still use percussion primers to ignite the powder charge. Electric primers exist but they seem to be a big step sideways in the evolution of gun technology. The percussion primer just has too many advantages, it's simple, reliable, and you don't have to worry about a dead battery in your gun.
Daisy invented a case less round with a solid propellant that was diesel ignited by a strong spring air rifle mechanism. It too died a well deserved death as it was the classic answer to a question no one asked. Who wants a single shot .22 that's as hard to cock as an air rifle and ammo that you can't allow to get wet during a rainstorm anyway?
