Sorry A37575, your argument is not specific to mixture cuts. If you use throttle to simulate engine failure and the engine doesn't pick up when you move the lever back up, then you still have no useful power. The mechanics of the throttle linkage and the mixture linkage are very similar, and neither is any more likely to fail than the other. Power is returned just as quickly whether you use throttle or mixture in the simulated failure. The gamble (as you put it) is exactly the same one, with exactly the same odds of losing.
There is in fact a considerable difference, in one case the engine is completely shut down & requires a restart & windmilling only assists the restart, in the other the engine is simply idling under no thrust power & will return to full power on application of the throttle.