My "theory" why an elevated rest typically will give better arrow flight is the arrow has much less contact with the bow. Less contact equals more forgiving for flaws in tuning or form.
And, I have NEVER seen any bow shoot better off the shelf than a rest. That is not saying you can't get excellent arrow flight off the shelf. Most of my bows are set up to shoot off the shelf.
But, my BOW, the bow I trust over all the others combined, the one that I know will survive any conditions in the wilderness I come accross, the one that will shoot a broadhead where I want it with feathers OR any vanes, the one that I would keep if I was only allowed one bow; that bow has an elevated rest on it.