Brass is formed several times for ammunition: deep drawn to forge a solid thick base with thin walls; rolled or swaged to hold the bullet; and one last time, when it's actually fired, to expand into and seal the breech of the barrel. It has an excellent combination of formability, machinability, ductility, strength, and also lubricity to move smoothly through the mechanism, and corrosion resistance to survive years in the field and remain usable.
I think blanks would still need to be annealed once or twice on the way through deep drawing? But maybe they can manage it in one hit. Huh, come to think of it, I've never looked up an ammunition manufacturing video. Let me see...
...Or even just an article, that'll do. Looks like four anneals total:
https://www.petersoncartridge.com/technical-information/drawing-brass/ For a rifle cartridge anyway; maybe a pistol round only needs three, maybe even two, but three more likely.
Brass can even be reused once, maybe even twice or more, if it's clean and not dented, and probably many times with additional annealing and swaging steps to keep it in tolerance.
Steel might be too strong, having difficulties in forming a thin shape, or fitting the bullet without turning up burrs (it's only soft lead, or copper jacketed, after all), or not conforming to the barrel well enough on firing, and obviously is prone to rusting. Hmm, I see plenty of hits for steel rounds, so it's definitely used, and many of those issues might be mitigated say by lacquer to improve lubricity and corrosion resistance, but given the quoted text on most hits, it seems it tends to be poor quality, loose tolerance, "dirty", etc. That kind of goes with it being cheaper in general, but perhaps that also speaks to manufacturing variation due to material differences. Steel is quite ductile, but not as much as copper and alloys are; it probably needs one or two additional annealing steps to complete (and higher temperature is required to anneal steel). Or maybe they manage with a less strenuous process, like rolling seamless tube down to shape, but maybe that only works with certain types of bases.
I'm quite removed from gun lore, myself; this is more motivated by the metallurgical relevance. Others can chime in with actual practice.
On a related note, I wouldn't at all mind tin-plated steel crimp terminals, for connectors carrying signals; it should be workable, and perhaps they could be cheaper, or the higher strength allows more flex and thus vibration resistance, or contact pressure (but then again, it can't be too high where the tin plating gets squidged out), so there could be reliability gains; but probably between the ductility, and the dissimilarity to the wire it's crimped on (crimping pressure/depth needs to be more carefully calibrated to avoid pinching through the wire entirely), this just isn't a good idea. But maybe they do indeed use it some places, dunno.
Tim