I guess it comes down to powder since it was used for many years for structural strength but that was with blackpowder and since smoke-less powder needs less volume to get the same effect, lower brass could be used but I wouldn't trust a 100% plastic shell if for nothing else but extraction. Everything said is right and wrong but it depends on the type, quality and era of shotgun shells being used.
Close, but not quite right about the brass height.
High brass shells are an artifact left over from paper shotshells. On a paper shotshell, it served the purpose of keeping the powder from burning through the hull when higher powder volumes were used in heavier load
BINGO!
Sorry for the thread veer (nearly unavoidable talking plastic cases), but lets get this out of the way. Shotgun shells for decades were made of fiber, "paper", and brass. Roll crimps and over the shot card wads. Thick fiber over the powder (under the shot) wads, a fiber "base wad" that was part of the case head, and the brass case head on the outside. NO plastic shot cup, hulls, or wads.
Target and light field load cases had a high base wad, which left a much smaller room for the powder. This was intentional, they were light loads. They had low brass case heads, that was all that was needed for reliable head space and extraction.
Heavy field loads & slugs, had high brass for more strength, because the cases had low base wads inside, to allow for more powder. A benefit, as already noted was the prevention of burn through.
By the 1950s, plastic was the new high tech and everything you can think of was being made of it. Not everything worked, but in shotshells, it did. This new plastic case ended the burn through problem, and seemed plently strong for the low pressures involved.
However, its tough to make a plastic that is both soft (flexible) and hard (ridgid) where it needs to be. Plastic can be hard enough, but gets brittle, and the small rim of a shotgun shell has to be fairly rugged for its size. Too hard and it breaks, too soft and extractors slip off or pull through.
The brass was kept, and the traditional height was kept also, as a simple visual and tactile identification. Its what people were used to seeing, and trusted.
Some all plastic shotshells have been done, a Winchester one was very popular, but only in target loads, as far as I know.
CCI has a large line of aluminium cased handgun rounds, under the name Blazer. They are berdan primed, specifically to discourage reloading. They cost a little less than brass cased ammo. I haven't bought any in years, but back before the great ammo shortage and "Obamascare", they were about a buck less than regular ammo.
They work pretty well in revolvers, and short auto pistol cases, but not well with long auto pistol cases, (magnum revolver rounds in auto pistols).
Plastic can be alot of things, nearly all things, but its forte' is being one thing at a time. And its easily moldable, because its one thing at a time (homogenous). Plastic doesn't temper or anneal well, compared to metal. Its flexible, but not ductile like metal. Remember cases have to expand to seal,(and release the bullet) and then spring back to allow extraction.
At low pressures this isn't much of a problem. But high pressures tend to "weld" the plactic in place. It takes a lot of work to come up with a formula plastic to work like brass, or even steel.
Apparently it can be done, as the plastic .223s reported in this thread proove.
But, how practical (including expense) can plastic cased ammo be? As mentioned, how do you make it hold a conventional bullet the way metal does?
I'm a dedicated reloader, who doesn't even much like berdan primed brass, let alone steel aluminium, or plastic cases. It may not be true, but I believe it is, that I get more out of my invenstment in ammo than someone who shoots throw away stuff.