Proposal: Change the mechanics of cool down reduction

Say for example you have the max cool down reduction (i.e. 40%) and you are Karthus at level 6 (first level of Requiem has a cool down of 200 seconds).

Instead of your Requiem spell countdown starting at 120 seconds due to cool down, my idea is instead to start the countdown at 200 seconds, but the speed of the countdown itself is increased by 40%. In other words, 1 second now becomes 0.6 seconds in terms of the count down.

Why do this? This way, any champion immediately benefits from acquiring items with cool down reduction or obtaining blue buff. Right now, this is not the case. If Karthus uses his ultimate with 0% cool down reduction and then acquires 40% CDR, he has to wait the full 200 seconds to benefit from the CDR on his ult.

So essentially, none of your spells' cool downs change. It's just the count down rate speeding up with CDR. Thoughts?