Large, yes. Specialized, no. The same sort of presses that make cartridge cases also make lipstick tubes, little flashlight bodies, etc.
Producing tubular items from malleable metal is a pretty common operation.
Overall, if you had a 50 ton hydraulic press (a power press would be nice) and some machining capability, you could make your own dies and stamps for making cases in much the same way as it is done in large scale processes.
Still, with a lathe, you could make your own brass. The reason why the industry doesn’t use turned cases is obvious: the amount of waste compared to the final product is huge. With punching, drawing, etc, you have much less waste and higher throughput. Well, brass melts at a low enough temperature that with a heat treatment oven, you could melt down your waste and re-cast it into rods for making more cases. Just keep the swarf clean of other metals, that’s all.
With some thinking and ingenuity, one can make a lot of stuff with very rudimentary tools. The trouble is, the US has become a nation of cubical gophers, and forgotten how to make stuff. With what I’ve learned in the last 10 years, they could go ahead and ban guns, seize the lot... and in a month, I’ll have a working rifle again, made from a truck axle and scrap steel, along with ammunition.
It’s not that difficult, really. Yes, it would take a bunch of work. But it is a LONG way from being “impossible” and it is difficult only the first time. After that, a whole lotta light bulbs go on over your head (unless you’re a complete mechanical klutz) and you see how to do not only what you’re trying to do, but a great many other things too.
Something that really opened my eyes was going through the Browning Firearms Museum in Ogden, UT. They have the Browning Bros. shop re-created in a nook off the main gallery floor. You’d be amazed at how little power tooling they had. They had no mill. They had only a lathe, and a small one at that - something about the size of a South Bend 9” swing, with a long-ish bed. From looking into their shelves of stuff, I could see that they had fixtures for doing milling on the lathe - they had no mill anywhere in their shop. They had a large collection of hand files. And with this minimal tooling, they produced one patentable firearm design after another.
If JMB could do it, so could we.
What people need is a lathe and some training how to use it. Once you have a reasonable lathe, suddenly the world of mechanical widgets swings open as tho you said some ancient magic words.
I'd say a stamping press is pretty specialized. You find very few of them in home shops, but I'd like to hear how you plan to make smokeless powder and the lead styphanate for the primers.
Have you ever tried doing this on a lathe? You'd still need some sort of press to get the tapered shape, but ignoring the expense and the need for a press anyway to get anything except straight sided pistol cartridges, think of how long it would take. I just made some stainless steel repair parts about the size of a .44 cartridge on a lathe, parts that didn't need the precision that ammunition needs and didn't have to be tapered (replacing a broken aluminum boat hatch hinge - no longer available), and making half a dozen of them took all day.