Most cars are closed loop or stoichometric for 70% of the load range. They go into open loop at higher load.
DI increases the cooling effect from injecting the fuel. It allows for a higher compression ratio to be utilized.
Our engines(Otto Cycle ICE) are most energy efficient at full throttle. But are more fuel efficient the less RPM with the most throttle for a given speed. The energy efficiency decreases as it leaves the peak efficiency zone which is like an island (BSFC chart:
Ecomodder). A smaller displacement engine increases the load for acceleration and cruise.