I think it might be worthwhile to consider in a fluid dynamics sense that the bladder is what provides the proximate gust of air that permits the attack it DOES have to actually happen.
When that big valve/reed clearance opens, the air must rush through – if there’s no spring-loaded proximate air reservoir to dump, it would start swinging much more slowly.
This is synchronous with how the attack is so gentle if you don’t build pressure before you hit the key. Effectively you could say that is the effect you get without the bladder under tension.
A not dissimilar effect as the air tank on the trailer of a big rig, that provides a gust of air in close proximity to the brake actuators when needed, so that the truck can maintain control better. Or any pneumatic system with storage bladders/tanks close to the point of use, so that the working fluid can fill the gap without needing to chain-release all the way back to the main source with the accompanying velocity-related drag and pressure drop.