I fully agree with everything else you said and I am familiar with this definition of overbalancing.
I suppose this could be done relatively easily if, for example, the ambient pressure side of the piston head (in a piston reg obviously) were slightly larger than the compression chamber/IP side of the piston head. It would require a slightly stepped design, a matching step with adeqate working range in the body or cap of the reg and an extra piston head o-ring and would neccesarily increase the complexity of the design. But I don't see the point - it is not worth the trade offs.
A 20% increase in IP would be about a 12 psi difference from the surface to132 ft. That 12 psi increase in IP over ambient would require the second stage to be detuned so that it does not freeflow at depth (a very bad place for that to occur). It has been pointed out a couple times previously in this thread that even a balanced second stage still must be biased with a smaller than ideal balance chamber to ensure it still functions like a downstream second stage to vent excess pressure in the event the IP becomes excessive.
There is no doubt some slight benefit in increased flow rate due to the 12 psi increase in IP that would help offset the effects of increased viscosity of the air at depth. And the second stage would in fact breathe easier at depth due to the increased IP.
But on the downside, there are better ways to deal with viscosity such as larger and better designed air passages that will as a side effect improve flow rate in all situations. And the "improvement" you would see at depth in terms of improved cracking effort is instead just the removal of the detuning you end up with the lower IP's found at shallower depths.
It is in my opinion a far better approach to have a very stable IP (relative to ambient pressure) that is not affected by either depth or falling tank pressure. If the IP remains constant relative to ambient pressure (eg. 140 psi greater than ambient at 0 ft and 140 psi greater than ambient at 132 ft) that will enable precise tuning of the second stage for max performance and ease of breathing at all depths.