I think we are mixing up terms here. Springiness = less spring-back.
Brass is hardened by working it. Imagine you have a case you just fired for the 10th time without annealing. The neck OD is say .342, and you want to re-size it with a bushing of .338 When you try to re-size it, the draw on the press is very hard. You then measure the brass and is .340 This is spring-back. The brass is hard and does not want to change dimensions. When you pulled the case out of the sizing die, the brass "sprang back" to close to its original OD and didn't stay at the bushings .338
A common complaint of guys when their brass needs annealing is they report that sized brass isn't holding the bullets after seating. That's because of the spring-back, the neck's are not sizing completely.
Annealing softens the brass, making it more malleable, more "springy", and more willing to change shape.
If you eliminated the spring-back entirely, you couldn't have any neck tension. When you seat a bullet, the OD of the bullet is slightly larger then the ID of the neck. If the brass had no spring-back, seating a bullet would be the same as sizing the neck with a bullet as a mandrel, and there would be no interference fit to hold the bullet.
Other then that, I agree with you completely. Anneal before sizing and anneal often.