The trick is having a large buffer, so that typically the engine can operate at the point with the best specific fuel consumption or shut down entirely. Getting energy from the engine to the wheels is less efficient than a mechanical transmission, but the increased average efficiency of the engine can more than offset that.

Still seems like a traditional hybrid would be more efficient. I'm not sure what's gained by removing the mechanical coupling altogether (other than cost/reliability).

Honda has an interesting solution in their latest gen hybrids, where the electric motors power the wheels at lower speeds, the combustion engine runs at its optimum RPMs as a generator while the electric motors are working, and at higher speeds a clutch activates that changes the coupling so that the combustion engine directly drives the wheels.

Whatever the Prius HSD does is great. It'll do 50 MPG city and highway. No clutch at all.