Dick,
I think the incorrect statement in your idealised engine is where you say:
At the end of the exhaust stroke this has been ejected.
This is not quite true. The exhaust stroke is (inevitably) the same length as the compression stroke, and the cylinder is not "empty". What remains is (some of) the burnt mixture; you will have the volume that corresponds to the cylinder volume at the top of stroke, and the pressure of the gas will be approximately equal to the pressure in the exhaust manifold. To the extent that the pressure in the exhaust manifold is higher than the inlet manifold pressure, the next induction stroke cannot draw a full cylinder of mixture in for the next cycle - in fact no mixture will be drawn until the piston movement has equalised the pressures. That is why the quality (and pressure) of the exhaust system can affect the performance of the engine.
Of course in a real engine, it is possible to "tune" the exhaust system so that the momentum of the exhaust gas and the resonance in the manifold presents an artificially low pressure at the exhaust valve and thus achieves a much better than expected purge of the cylinder - but now we are confusing the trivial model with reality!