[IAmEveryone]

I believe hospitals do use systems with a single, central supply of pressurised air.

However, I'm also getting the sense from reading about these efforts that creating pressurised air is the easiest part of the setup. You need to control that pressure with a precision unlike any other application of air pressure. Just alternating high and low pressure isn't going to work, for example: you need to slowly ramp up pressure, then slowly release, on a specific schedule. Every patient also has individual needs, to the point where even for two people of the same gender and similar age/weight, the settings ideal for one might kill the other, and vice versa.

If I understand it correctly, these machines use feedback loops with sensors for blood oxidisation, acidosis, the elasticity of the lung, and other factors. Without such mechanisms, you'd be constantly adjusting the settings––consider a heating system or AC where you can't set the desired temperature, but only flow rate and power of the heating/cooling instrument. You need constant attention to keep such a setup within a comfortable range. And that attention will also be in short supply when hospitals are overrun.