I've also had short barrel cap and ball temptations, especially for the Colt style because I can change the barrels.
Then better sense usually hits me.
Like James K said, loading becomes a problem on the gun. You can always remove the cylinder and load using a stand, but with the Colt's, it's too time consuming. Again, the ease of removing the Remington cylinder makes it worth considering.
But cutting down a perfectly good New Model Army is a tough pill to swallow. However, a snub NMA and a gated conversion makes for one heck of a pocket sledgehammer compared even to modern revolvers like the Charter Bulldog and Taurus Public Defender.
So is a cut down 1851 a good idea? Depends, how much money does it take to part with until the point it becomes a bad idea? If you buy a spare used barrel, you're looking at $100 right there. Then there's the work you have to do chopping it down and doing it right.