Most of the time (your mileage may vary) a 44-40 has very little, if any, fouling in the action. Most guns finish a full CAS match looking like they have just been cleaned.
I like the idea of chambering a fired case and running a wet patch thru the bore every so often. If your hitting the targets without problem, you may not want to bother. If you shoot APP, you may not want to bother. If your shooting Big Lube bullets, you may not want to bother.
44-40, 38-40 and 32-20 are the cats meow for BP shooters.
I, on the other hand, shoot .45s, and don't bother. Since I live with a lot of blow-by, I do squirt the Carrier Block every now and then to keep the gun running smooth.
Coffinmaker
PS: as you peruse the stuff here for Darksiders, pay particular attention to Lefty Dude. Nothing but GREAT information.