Apparently, there's a misunderstanding as to to relationship for "elastic" to being "springy", huh?
"Hardened brass" resists movement and wants to retain its shape when force is applied to it and the term "springy" can mean how far the material can bend before it doesn't return to its original shape, which is what I hear you saying. Annealing makes the brass more "elastic", meaning it's less resistant to movement. Like, fully annealed brass has little resistance to movement and will be more like damp clay. What we try to achieve when annealing our brass is something in-between "hardened brass" and fully annealed brass. The main goal is for consistency in how the neck holds the bullet, but not so loose that the bullet will move in the magazine due to recoil or for any other reason before being fired.
Bottom line . . . our annealing process makes the brass more elastic and less "springy".