The folks who have done the most scientific work on annealing brass cases are Annealing Made Perfect (AMP). There should be no bias in their recommendation because when you anneal does not affect their potential sales. Their recommendation?

"Annealing should always be done before resizing. This eliminates spring back, and ensures repeatable and accurate shoulder bumping and neck sizing."

Annealing isn't just about case life. If your goal is consistent neck tension, it's pretty simple to conclude that annealing should be done after each firing.

Is it necessary? That depends on you, your goals, and your results.