Does wrapping overgrip up onto the shaft affect the flex of the shaft when swinging the racket? I suppose if the shaft flex point is above where the grip stops then it won't matter much, but if the grip covers the flex point then will it feel slightly harder to flex? Of course the more overgrip you use, the more it will affect the balance point, which is probably much more noticeable than any potential increase in shaft stiffness. I think I've seen a grip wrapped up to half the length of the shaft before.
Wouldn't imagine the overgrip being rigid enough to change the flex of the racket. Possible for those thick PU grips but doubt a thin overgrip would.
Not a scientist or anything, but if Kinesio tape can hold your shoulder and knee ligaments while you're at the limit doing sports, a tape may add some resistance, and perhaps making the shaft ***slightly*** stiffer. That said, whether at all it will be noticeable in your hands is another debate.
Next thing are aerodynamics. Wrapping up to the shaft would makes it bulky. If the aim to add stiffness to shaft, tootpick for structural strength + electrical tape to put it together would give more stiffness but not to bulky. Tho it would look somewhat ugly.
In the future there will be a fully modular racket where you can change the head weight, shaft stiffness racket length