I shoot a lot of black powder in cartridges, namely 45-70, 45 colt, .410 shotshell, and 12 gauge.
Any non-gas operated gun CAN fire black powder, with some caveats.
Many more modern cartridges just don't have the cartridge capacity to be useful with black powder. The old black powder cartridges, the most commonly available today being 45-70, 44-40, 45 colt, 38 spl, all shotguns shells. There are others, but those are the most common. These rounds are just as effective with black powder, as they are in their standard smokeless loadings, and are often loaded to +p pressures with smokeless. The factory smokeless loads in these cartridges are actually loaded to approximate the BP load, and are even down loaded a bit. Some cartridges designed for smokeless powder will suffer piss poor performance with BP, some possibly dangerously so.
Some actions lend themselves better to black powder, any single shot, double barrel, lever action, or bolt action can do well with bp, as long as the cartridge chambered in them is also suitable. Recoil operated gunsncan be dirty to the point the jam in short order, gas operated guns even more so, however, these guns are normally chambered in cartridges that don't work well with BP, the ruger carbine in 44 mag being the notable exception off the top of my head.
Some cons to black powder:
It is dirty, but when fired from cartridges it burns much more efficiently than fired from muzzleloaders.
It is smokey, yet again, from a cartridge it is noticeably less than a muzzleloader.
And , it has to be loaded into a full case, which means if you want to get more power than standard, you have to go to a longer case, less powerful you have to use something to fill the space left in the cartridge. There are extransteps to cleaning then brass when use with bp, I won't go over that here, other than YouTube abounds with info, which is where I learned.
The main pros: cases last a long time. In my 45-70 I was getting 4 or 5 loadings from my cases with +p+ smokeless loads, 8 or 10 with standard smokeless loads. I have cases that have been loaded with only BP, that have been loaded 20 times. BP is versatile, there is no smokeless powder that I can use, and get good performance out of rifles, pistols, and shotguns. In shotguns, you can use plastic hulls, but I prefer all brass hulls. BP is hard on plastic hulls and components, and are pretty much limited to 1 reload, maybe 2, and you can have some considerable plastic fouling in your bore. BP burns hot and slow enough it melts the plastic.
Reloading shot shells can save on components, and therefore cost. If you have ever taken apart a modern shotshell, there is a lot of dead space inside which the components take up. Reloading a shotshell requires that then powder charge, wads, shot cup, and shot all come out to the right height to get an proper crimp on the plastic shell. So you are often having to match certain shot cups to certain hulls.
With bp and brass hulls, it is simplified. I use magtech hulls for 12 gauge, and hulls I made for 410, made from 303 British brass. They use Large pistol primers, the same as my 45 colt. I prime the hull by hand pressing the primer into the pocket, then using a wooden dowel to tap the hull down onto the primer on a flat hard surface, then i pour in the measured charge of bp, then seat a cardboard card I cut, usually from non-corrugated cardboard which is destined to be burned or hauled off, using the dowel. Then I put in a couple wads which I cut from Styrofoam meat trays, or from corrugated cardboard. Then I add the shot, either a measured charge of bird shot, or by counting buckshot pellets. Over the shot I put another cardboard card. The card is sealed by running a bead of some sort of glue around the edge. I've used white school glue, wood glue, silicone, and white bathroom chaulk. Technically if they are not jostled around they won't need sealed, but I always do. Load column height matters not. In will usually finish it off by writing the shot size on the top card with a sharpie.
My loads are: 45-70: 70grains of ffg and either a 405gr homecast lead bullet. 45 colt: 40gr ffg and a 250gr home cast. 12 gauge: 70gr of ffg, and either 1 ?oz of 7½, or 9 pellets of 00. 410 is 30gr ffg and ½oz of 7½ or 3 pellets of 000. I haven't started casting buckshot yet.
My bullets are cast from scrounged lead, old plumbing fixtures, corroded fishing weights, roofing lead, old lead pipes, wheel weights. When I see lead, I grab it, and I will go by the scrap yard and buy lead people have sold for scrap. I have a lot of lead melted down, cleaned, and cast into ingots.
Lubricant for the bullets can be made in advance and stored, or beeswax can be used.
Clean up can be simplified too, with black powder. Soap and hot water. You don't need special black powder solvents. Then clean like normal, if needed. I usually just swab out the bore with hot soapy water till the water runs clear, wipe down the outside with a wet soapy rag, and the internal parts, then oil.
You can still use jacketed bullets also.
The NEF/H&R guns jack did a podcast about are great platforms for bp, and they are chambered in several cartridges suitable for bp. (357 mag, 44 mag, 444 marlin, 45-70, 500 s&w, 45 colt/410, and all the shotguns.