You disconnect the autothrust then push the levers into MCT to obtain max continuous from the remaining engine. As you say the elevators control the pitch to maintain your chosen speed, depending on your strategy. MCT gives you the lowest rate of descent for the selected speed, with autothrust on it would, as you said, go to idle. So MCT increases your range, compared to idle descent, as you drift down to the one engine inoperative ceiling. There is a note in the QRH to engage autothrust again when the descent rate is small. If you were over your chosen divert airport, if indeed you decided to divert, then an idle / autothrust on descent would reduced your descent time - I suppose the QRH is designed for the worst case where you need to maximise range.