[dcb]

I could see using a vvt on the exhaust stream, to add a flexible amount of torque to the drivetrain or something.

But since throttle losses are not necessary (direct injection) it would be best to eliminate them alltogether.

The heat energy on the intake would have to be via heat exchanger, which is going to lose significant energy in the process, the exhaust gas specific heat is not going to be room temperature, and the turbine intake specific heat is not going to be near what left the exhaust valve.