Stuart_ G förklarar det bra. Shaft load.
As other’s have said it’s mostly a “feel” thing. And that’s because for some people (not everyone) the feel of the shaft loading and unloading can be used as a type of feedback from the motion to help individuals control the swing - especially different timing aspects of the swing.
For those that do not use that feel to help control the swing - the effect on performance is very minimal. Depending on the mechanics of the swing, it might result in the shaft adding a different amount of dynamic loft to the head at impact. But nothing that couldn’t be compensated with a change in head loft.
So some individuals will see zero effect on performance. Some might see a noticeable but minimal effect. Then there is a group of individuals that have to have the stiffness profile in a certain specific range in order to get any kind of consistently good swing.
If you are “missing something” - it likely means you’re not in that last group - a fact that you can be very thankful for 
