Boost Compression Ratio Calculator (rbracing-rsr.co
What you relate is in aviation called Density Altitude. High and/or hot reduces air density. A heavy loaded aircraft may not be able to sustain flight due to reduced engine power and reduced boyancy in the air.
A supercharger will increase power but suffers power loss at altitude. A turbocharger maintains power better in the thin air as it will spin faster to maintain manifold pressure.
The WW2 RR Merlin engine and some others had 2 stage or 2 speed superchargers that ran at a lower speed at lower altitude but changed up at higher altutude. This maintained power up to FL 300 or 350. Add 2 zeros for altitude.