So what our examples are missing a couple key points:

1. air density linearly decreases for a given pressure as temperature increased. Using the same turbo or supercharger, doubling the boost will likely come with increased air temp, so you aren't actually getting double the density. The temp can be calculated from the compressor map, too.

2. The backpressure, which you touched on earlier, actually hurts more due to work lost to pumping losses. The indicated power keeps going up but the engine is wasting more horsepower just overcoming the backpressure.