and anything is an improvement over not doing any annealing
Food for thought... I hate long posts but this doesn't get pointed out enough...
When the cartridge is exposed to 55k PSI several times, the whole cartridge starts to change, but the necks in particular start at about 100HV and trend toward >150HV.
(The ratio of elastic to yield also changes with the cold work but we tend to only hear about HV because the tests for strength are very difficult but hardness pokes are easy.
There is a relationship between the cold work, yield strength, and hardness, so we use HV to track the brass but the yield strength is very important to performance and life.)
With "good" annealing you can keep that HV close to the 100 level and in theory keep the neck cold work level from drifting up, and in theory when done properly keep the batch variation small so that the neck prep gives a consistent result. (We won't derail this thread with the debate about the relationship between neck prep consistency and accuracy.)
When you don't anneal, the brass batch trends up in hardness value due to cold work but part of the question here that I am drilling down on is the consistency within the batch.
The firing and prep cycle may cause the average value to climb, but if you consider variation within the batch, many folks who do not anneal learn manage their case prep for the average trend in cold work as their brass changes and do just fine performance wise since the variation within the batch is still small.
Here is the rub....
If you don't anneal well, and your brass batch starts to get variation as a result, you would in theory be better off not annealing. If you anneal properly, the theory is you stay near that 100HV and maintain consistency, and better brass life and better accuracy as a result.
I am not trying to persuade you to anneal or to not anneal, but I am pointing out that bad annealing is in theory worse than no annealing if you allow it to cause a greater variation.
Since every context is different in terms of brass, chamber diameter, case neck prep process, etc., there is never a single answer to the question of annealing or not annealing, or even what kind of annealing.
Since it takes many cycles to fatigue the brass to the point of split necks, there is an additional question of the value of annealing in terms of brass life.
I will generally suggest you test by running your best process with one batch being annealed and the other batch not annealed and see how they run for say 10 cycles or more and then decide. I am all for annealing in the right context, but have seen folks frustrate themselves with annealing just as often as it has helped them. The difference is the variation in the results. YMMV
Merry Christmas and Happy New Year!