If you heat brass the components realign. At that point why not let it cool? Why quench it?
Re-dissolve might be a better term than re-align.
Breaking up the larger crystals in the solid solution is a big part of it (although they call it "recrystalization").
And, no, I am not a big expert at this but that is how I visualize what I have read about it.
Copper Alloys and Its Heat Treatment | Metallurgy
"After annealing, the articles may be cooled at any rate."
The main reason you quench cartridge brass after re-annealing the necks is to prevent the heat from
traveling any further down the case and softening the lower body or base.
Wildcats made from rifle brass that have had their heads cut off have to be annealed so that the
new "necks" are soft enough to resist splitting (see picture).
New cases are annealed more than once during manufacture as they are drastically work hardened during the draws.
They are somewhat quenched right afterwards but that is an acid bath mostly to clean the oxides off.
Not sure how much, if any softening, the bath contributes.
The folks at Starline would be the ones to ask about this.
My 1995 Triumph Thunderbird uses a copper washer to seal the oil drain bolt.
The newer kits have an aluminum washer you just throw away after 1 use but I like the older method.
This entails annealing the washer to red hot in a torch before each re-use.
Here the main reason to quench is to minimize and flake off the oxide coating before use and to keep anything from getting burnt.
It will actually stay somewhat softer if you just lay it down (carefully!).
I have not conducted scientific experiments to see just how much the quench affects the post heating "softness".
The heating/cooling cycles of running the bike over the next year hardens the washer
after it has conformed to the small tooling marks on the bearing surfaces.
The whole metallurgy of hardening is complicated and fascinating.
It's mostly based on crystal structure and how that changes under various forms of duress and chemistry.
I know just enough to be dangerous.
Maybe that's why the Wife took my blow-torch away from me?