There is a considerable difference between balanced 1st stages and balanced second stages.
The term balanced can often be confused for "adjusted".
Some first stages, such as Sherwood's, "adjust" for the drop in cylinder pressure as the gas is used.
This is to compensate for the fact that when the cylinder has 3,000psi in it, it will be exerting a greater pressure on the piston face (which is a given surface area) than when the cylinder only has 300 psi in it.
The first stage spring is approx. 120 psi, this, plus the 20 psi from a full cylinder, (3,000 psi) exerted on the "flow by" piston face, = approx. 140 psi.
On for instance, the same Sherwood valve, as the pressure in the cylinder drops, so the "knife edge" that seals against the piston seat moves away from the piston (again, which is a given surface area), thus assiting the spring as now there is only 1 psi linear force exerted on the piston by the gas.
In addition to this "adjusting" diving regulators then need to stay a certain pressure ahead of ambient pressure.
Apeks suggests an interstage pressure of between 9 and 10 bar, say 9.5 bar, this is then kept at 9.5 bar above ambient as you go deeper or shallower, so your valve allways gives you 9.5 bar over bottom pressure.
There are various reasons why manufacturers suggest and use a particular interstage pressure, such as trying to reduce the cooling caused by gas expansion, longevity of seat materials, i.e. reliability, ease of manufacture etc.
There used to be a Norweagian valve manufacturer that had a philosophy of having very low, 7 bar I.P. to help reduce the effects of cooling, i cannot remember the exact name, but they worked well. Likewise some Posiedons have a high 12 + I.P. and there valves work well too.(usually !)
All the manufacturers belive thier method is the way forward, so i would give a great deal of thought before i changed a valve i breath off, as oppossed to used for say, an argon cylinder.
I think the AP oxygen valve IP is not so much concering the volume of gas, but more the force exerted on the solinoid valve, and not having to great an IP pressure causing it iether to jam open, or more likely, not open at all !
Now a balanced second stage is a different animal ....................