I think you may have led me astray with that first comment, and that my intuition was probably correct. How exactly does one purge the ballast tank with the air tank? Would you not actually need an air tank that has (at least) double the pressure of the outside water? Then to clear the ballast tank you would open the air tank, the
higher pressure air would then force out the lower pressure water (this is clearly why it can't be the
same pressure as implied in your first comment), and then when you're done you have two tanks (your air and ballast tanks) both at 380 bar, assuming they are both the same volume.
In that case you'd actually need a PV rated for 740 bar, which seems outside our current materials science abilities. In fact (and I'm still mostly just spitballing here, not actually doing any math), I assume you actually need a purge tank with a pressure much greater than 2x, otherwise you're just cancelling out your ballast with your air tank, right?
That would track with using this system in submersibles that are operating at ~300m and not for things like this which are trying to operate at 4000m. At 300m you could have a 400 bar COPV for emergency purging that is only 7.5% the size of the ballast tanks, which sounds practical.