It just works so well.
When they first came up with the idea of metal cartridges, they tried several things. They had cartridges made of wrapped wire. (Can't find a picture of that)
They had them made of metal foil. Second from the left.
Neither of these held up well to handling.
They thought they had a winner with copper, but copper gets sticky when it's hot, probably because it is a soft metal. During a battle, with much firing, the hot chamber caused the copper cases to stick, with the extractor ripping through the rim, and requiring the shoving of a cleaning rod down the barrel to punch it out. Kinda defeats the purpose of a repeater.
But the addition of a little zinc to the copper both made it harder, so that extractors did not rip through rims as easily, and "not so sticky", so it did not cling to hot chambers.
Wallah (that's French for "lookie here"), cartridge brass. Hard enough to hold together, soft enough to seal the chamber, strong enough to stand up to handling. Just about perfect.
They've used other things when they had to, but brass is so "just about perfect" that they keep going back to it.
Meddle not in the affairs of dragons, for thou art crunchy, and taste good with catsup - George of Lod, Year of Our Lord 297
I always take precautions.
Beware the Evil Bullet Fairies.