For several years my wife and I were moderators on a hunting/shooting/outdoor website called Modernsportsman.com. It's pretty much history now, since the owner of the site passed away. There's been as many billions of electrons wasted on discussing brass annealing there as we do on the subject of Rochester vs. Carter carburetors! Some reloaders swear by the procedure, while others swear at it. One guy who is probably a "train driver" in his daily life even cobbled up an automated process using two torches, a stepper motor, a rotating shell holder, and a timer. He claimed that manually heating cases with a single torch resulted in uneven heating of the case neck and inconsistent annealing results. Another guy who claimed he could load 1K rounds a day on a single stage press to support his participation in some sort of target competition he did claimed that annealing was unnecessary and shortened case life. Those guys reminded me of some of the off the wall stuff I see posted on Stovebolt.
When I'm doing some pretty radical case reforming for a wildcat cartridge like necking up .204 Ruger cases to .25 caliber for the ".257 Scooter" round I was involved in developing, I anneal brand new brass to reduce the neck-splitting problems we encountered while case forming. Other than that, I really don't see the advantage of annealing unless one is loading a round where new or once-fired brass is hard to find like the .43 Egyptian Mauser I load for. Bertram Brass in Australia makes a limited run of them occasionally, at around $5.00 a case. Shoot and reload until the neck splits, then grab another piece of brass out of the bucket. I've got couple of thousand once fired 7.62 NATO cases, and almost that many .30-06 and .270 cases stashed away. With those basic rounds for case forming, I can make practically every other case I shoot.
I once had a bunch of .30-06 match ammo loaded by the Lake City armory for military target competitions. They had the characteristic rainbow-colored case necks, indicating the brass had been annealed during manufacture, apparently to assure the proper neck tension on the bullet. LC Match brass is almost impossible to find these days. It's good stuff!
Jerry