Shuffle in All Random modes?

"Shuffle" means to put in a random order instead of picking randomly. So, what about using that instead of the current system?

Example: let's say you own

With random picking (the current system), you could get: Game #1 Game #2 Game #3 Game #4 Game #5 Game #6 etc

It does get boring to always play the same champion, especially if your pool is actually pretty large and that champion is not among your favorite ones...

With shuffling (aka "put all the champs in a random order"), you would instead get something like: Game #1 Game #2 Game #3 Game #4 /End of the random list, re-shuffling it/ Game #5 Game #6 etc