Cost per shot?

.44/100 is about $0.21- $0.25.

No shooting BP isn't cheap, but it's not exactly expensive either.
Some of the ways you can reduce the cost are -
Buy powder in bulk when it's on sale
Buy cast lead from folks who more or less cast as a hobby for a few extra buck and save a lot
Swing into the big box stores after the muzzleloading season is over when they put the Pyrodex (if you can stand it), caps, and other supplies on clearance sale.
Cut your own wads, that's not tough.
It's not going to be cheap without some work -
Cast your own balls, and recover them from your berm to cast again.
Make your own powder.
Make your own caps.

I am spending about 12 cents/ 20gr shot. Most of my supplies bought a while ago, cast with free lead and don't use wads,

I tried to estimate the cost for my .50 caliber flintlock and came up with a total of 43 cents, roughly.

Ball - 12 cents (haven't seen them cheaper lately)
Powder - 18 cents (50 grain charge)
Patch - 6 cents (pre-lubed)
Primer powder - 1 cent (at 3 grains)
Flint - 6 cents (figuring 50 shots per flint)

I can spend 3-4 hours at the range for about $10. I sure can't do that with any of my modern firearms. Most of them would easily burn $10 in ammo in 10 minutes.

Still less expensive than 9mm these days, and, even loading and shooting fast, how many can you put through your revolver in an hour? I can (if I wanted to) put a lot more bullets down range with a modern revolver so, the reduced rounds per hour makes it even less expensive to shoot and you still stay busy the whole time, swab, measure, card, wad, ball, cap, etc

d

I think that the low average for a .44 is closer to .30 cents per shot, and that can even be a lot higher if folks include sales taxes, shipping, wads and/or lube.

There's 233 - 30 grain loads in a pound of powder @ $20 per pound = 8.5 cents.
Caps cost about $8 per 100 = 8 cents each.
100 balls @ $12.50 per 100 = 12.5 cents each.
That totals .29 cents per shot.

Lubed Wonder Wads cost about 10 cents each which brings the cost to 39 cents for each shot, any sales tax brings it up over 40 cents per shot.
Add any hazmat and shipping charges and the price might easily climb another 10 - 20 cents per shot for an estimated total of 50 - 60 cents per shot.
And don't forget to add in the extra costs for making paper cartridges, perhaps another few cents for each round.

I shave my costs a bit off the rack rate. Wads I punch myself for maybe 3 cents each. I cast most of my own round balls and other projectiles for the cost of purchased lead. Powder, you just try to hit sales. When black mz was out there for ten bucks a pound, I bought the heck out of it.