No arguement that turbo's produce the most power for the least parasytic loss.
However the claim that they convert lost exhaust gas heat is only partly true, as they also increase blow down pressure on the exhaust stroke, which pushes against the rotation of the crank, thereby creating a relative small parasytic loss.
I did own a Toyota Soarer MZ20 which had the M7GTE motor and automatic transmission. While it was a very comfortable, high performance, reliable, true GT coup, it had two interelated drawbacks.
When pushing hard through corners, that required controlled acceleration for best results, it either kicked down a gear and came strongly onto boost, or it changed up a gear and lost boost, sometimes 2 or 3 times in the one corner.
The option of manual overide of the automatic was not that successfull, as the shifter was vague and the gate design poor, which meant that it was hard to know what gear you were in, and it was to easy to overshift and select neutral.
With a supercharger, I could have squeezed the throttle without a downshift and got controlled, instantainous acceleration.
The technique of allowing for lag, can be usefull on a race track, but it still does catch a driver out occasionaly, such as when moveing through slower traffic, and someone does something unexpected, or the competitive driver deliberately hesitates at a critical time and therefore baulks you.
Turbo's are more efficient, but at times, they do create drivability problems. A positive displacement blower and a turbo compounded could give the best of both, but with relativly high parasitic losses compared to straight turbo.
I doubt if it is worth the extra complexity and weight, but it will give better power than a roots blower and better response than a turbo. It will still suffer somewhat if trying to feather the throttle on an automatic transmission car through a part power corner.
To dogledracing's question, It all depends on exactly what you want to do, and what is the net effect all the compromises for your particular application. Isn't that about the situation with almost every consideration when designing a car, or just about anything else.
Regards
pat