like I implied before, an engine driven centrifugal compressor is a stupid idea on an engine that's designed to have any significant rev-range.
the only way that could work is to have an infinitely variable drive so that the compressor shaft speed was totally un-related to the engine crank speed, problem is that would be complex and expensive to make and keep efficient, which is why nobody has done it.
The Rotex solution (friction drive) is a bodge, they are very limited on shaft power ratings, and horribly inefficient in terms of a transmission system, quite apart from them being hopelessly unreliable.
As said, an electric compressor is the ultimate, BUT these are only just becoming feasible with the advances in small high power motors, however, they still need a hell of a lot of power to drive them.
what your missing here is that the shaft speed of the compressor needs to be load related, not engine speed related, hence why a turbo actually works really well, the shaft speed is a factor of load, not engine speed.
the current thinking is just to electrically 'boost' turbo's to get the response times down, then, taking this a step further, using the motor to regulate the shaft speed when the turbine is powering it (instead of using the wastegate), syphoning off the additional power to either store for boosting later or feeding back into the powertrain (be that powering engine ancillaries or the main powertrain itself).
in time, once the OEM's are doing this, the parts will become much cheaper.