Isn't it the case that this attack vector and almost all others are the result of the poor architectural choice made by the first and all subsequent CPUs - the mixing of data and instruction?
Modern processors are usually a hybrid, Harvard on the inside (with separate instruction and data caches), Von Neumann on the outside. But some processors (ex: DSPs) are pure Harvard and both styles have co-existed since the very first computers, the ones made of vacuum tubes and relays. There is no "original sin".