I'm pretty sure what Hinglander was asking is why the after cooler is such an advantage ?
If that is the case, cooler air is denser. A huge drawback to direct drive roots style SC's is the heat. They are all compressors, when compressed a gas heats, when released from a pressure vessel it cools. Think about your car AC and the cooler it runs. Now, put it on steroids, turbo. Yeah, I know, way over simplified for so many variables, but in concept its there.
Which sort of brings us if not full circle, at least part way, turbo's take plumbing, room for the aftercooler, superchargers take the drive system, plus plumbing, nitrous takes smaller parts, but it still needs to be hooked up right and set for the motor, well all of them need that. On nitrous, cheater systems get REAL creative.
So, which gives you the most for dollars invested ? Turbo motors can live a VERY long life, roots type suprcharger motors, not exactly your daily driver, centrifugal superchargers are in use on the new Mustangs and I think the Lightning ran them also. Nitrous ? Never seen long engine life as one of its advantages.
Again, this has been my personal experience. Your results may vary.