Several reasons. The first is fundamental: density is not really helpful for this sort of application. The work done in expanding material (including gas) at a

Several reasons. The first is fundamental: density is not really helpful for this sort of application. The work done in expanding material (including gas) at a given pressure is P dV, and the work done in moving material across a pressure difference is V dP. Notably, mass doesn’t appear at all here, so adding more mass or density doesn’t add energy storage capacity in and of itself. You can compute this more explicitly, and, for an ideal gas, the useful energy extractable from a tank of gas at pressure P (under ideal, isothermal conditions) is proportional to the change in log P. So it’s actually rather more important to achieve low pressure than high pressure. On top of this, there’s a practical consideration: the atmosphere is an effectively infinite source of gas at 1 atm. If you are working between high and higher pressure, you need two reservoirs. All you’re gaining is less temperature change per unit pressure change, but it’s probably the same amount of heat for any practical purpose, so you still need an intercooler of some sort for good efficiency.