here's the thing, none of them is like the rest. Brass, steel and aluminum all behave differently. They have different "coefficients of friction", so each one slides into, grabs, and releases the chamber differently. Different amounts of spring back after expansion from firing pressure.
Now, these things, (and some others) overlap enough that all three are used as cases, but each one has its own quirks, and applications where some factor outshines the others.
One of the big factors to many people is cost. Cost over performance. It goes bang, hits what you're aiming at, (or close) and costs less is a big thing for some shooters.
This is where steel cased ammo has its greatest appeal, it costs less, generally. And it works, well enough, generally. But its not as "good" as brass in many ways, and while possible its not nearly as suitable for reloading as brass is.
Steel cased ammo was essentially a military expedient that became a standard in some nations due to wartime material and production pressure.
Particularly the Soviet Union and its satellite nations. And Soviet designed arms since WWII have been designed to run on their steel cased ammo. This also means they work well with brass, but the reverse isn't always true.
Guns designed to run on brass may not do as well with steel. It's not brass. So the differences can affect things. Often they don't but sometimes, they do.
Those of us old enough remember when steel cased ammo wasn't a common thing in the US. That happened after the fall of the Soviet Union, when steel cased ammo came in by the shipload and sold dirt cheap, which created a demand.
Also note that steel case ammo is not available in all calibers. Soviet bloc calibers, and the popular US/NATO military calibers, and very little else. It is simply not made in other calibers. See much steel cased .357 magnum or .30-30 Winchester?? I don't. Most of it comes from (mostly eastern) European (or Asian) factories which were originally set up to produce Soviet type military ammo. Many have expanded to produce 5.56mm, 9mm and 7.62NATO but few go beyond that. The market just isn't there (or wasn't before the virus, now I'm sure people would buy steel just to have ammo...)
Aluminum is used by CCI/Speer for some handgun rounds under the brand name "Blazer". It hit the market as a cheap (and non-reloadable) round before steel cased stuff was available in quantity in the US.
It was designed to work, ONCE, deliver adequate performance, and be cheaper than regular brass. It works fairly well in many guns, but not all. Does fine in manual repeaters (revolvers), and does well in the short cases most common in semi auto pistols. Doesn't do so well with long cases (like .357) in semi autos. Not at all usable in my .357 Desert Eagle or Coonan semi auto pistols. Rips rims off, or extractor tears through them. (not hearsay, my actual experience)
I believe this is because aluminum is not as "slick" as brass. I think aluminum doesn't release and spring back at the same rate or amount as brass and this results in extraction issues in SOME semi auto pistols. In "short" semi auto cases such as 9mm Luger and .45acp aluminum generally works ok, but with magnum length cases in semi autos, not so much...Also, note its not used in rifle calibers to any degree. Its just not suitable, or so it seems to me...
The virus and various buying panics have skewed the situation, and today I can understand people buying and using whatever they can get, But before that, I just couldn't understand why people would spend the best part of $1000 on a gun and then run the cheapest crap ammo in it to "save money".
I'm a dedicated reloader, have been since the 70s. If I get a gun that shoots boxer primed centerfire ammo, I'll get dies for reloading it.
I don't shoot Blazer (aluminum) or steel cased ammo in my pistols, or buy berdan primed brass stuff, You do what you feel best.