Superchargers are used in some cars due to the lag. Yes, even in modern engines it is still there. It is just a design issue. The turbo can be sized to give power at the high end or at the low end. Or, you can have multiple smaller turbos (costly).
Turbos are more efficient. You can run numbers for that, either engineering energy balance equations or just look at fuel consumption for equal power outputs. It is no surprise that turbochargers are used in aircraft piston engines and not superchargers (except for a few cases, some of which used both supercharger and turbocharger). Diesel trucks are another good example. The only ones using superchargers are Detroit Diesels, which are also 2 stroke engines and are known for high power and high fuel consumption (those superchargers were also the basis for most of the superchargers used in drag racing). FYI, DD engines use superchargers because at lower engine speeds the turbo does not put out enough compression for the 2 stroke process to work well (they need a lot of scavenging). DD engines is used in a lot of the Army's vehicles, from the 3cyl engine in the Gamma Goat to the 6cyl in the M113 APC to 8V92T (supercharger and turbocharger) using in some of the trucks and self propelled artillery pieces.
Early turbos were not that great on cars or trucks or bikes because the technology was not there for really high speed turbos, ie, smaller and more responsive as well as better performance across a wider RPM range. They also had trouble with how to manage the heat of the bearings cooking the oil. Fuel management was another issue since they would have to run richer, burning even more fuel.
Much of this has been addressed, but, for a pure sport bike a supercharger would be required, simply because of throttle response. At those power levels even the tiniest bit of lag would make for a bad day. Folks who race bikes talk about how sensitive the throttles are now, eg, a tiny movement of the throttle means smoking the rear tire or keeping it on the track. Lag there would make that even worse.
For sport touring a turbocharger would be far and away a better choice if you really needed more power out of your smaller displacement motor. But, it is easier to just make a larger displacement engine and not have to worry about all the hot exhaust ducting, turbo placement, and keeping the bearings cool. Not even counting the cost difference.
Reliability? Turbos these days are more reliable than many other parts of the car. My Subie WRX now has 190k miles on it with no engine work at all. It has not been 'raced' since it passed the 150k mi point. And, it is not even stock. Some upgrades pushed the 2.2L engine to 320hp from the 275hp stock output. I am more worried about the transmission on the car than the engine (the early WRX's were known for eating transmissions).
So, would I like a turbo sport touring bike? As a mechanical engineer I'd love one. I drooled over the Honda 650 turbos when they were introduced. Would I buy one? No. Too much extra complexity and heat issues on a bike with very little payoff. I'd rather just get a bit bigger motor.
Would I like a supercharged bike? No. Car? Maybe. Eaton made some really neat little superchargers a few years ago that had some nice features. Like a cutoff and bypass for low throttle conditions. I think it was used on the Ford Thunderbirds from a few years ago. My BIL had one and finally got rid of it after it passed 200k miles. But, he also used to comment on the poor gas mileage at freeway speeds.
Sorry for the longish post. Just an area that I am really interested in.
