Maui.
When using the mixture, you do have the ability to restore, and within a poofteenth of a second of the time it would take with throttle
Aircraft gets airborne, gear selected up, blue line attained when instructor cuts the mixture. Student whacks on full wrong rudder (been there-done that) so instructor takes over control with IAS decaying alarmingly. Instructor has one hand on the control wheel real quick and then to re start the failed engine has to (with one hand) close the throttle of the "failed" engine, push the mixture control from ICO to rich, then rapidly introduce full throttle while at same time counteracting the sudden yaw caused by rapid application of full throttle on the previously failed engine.
And you tell me its all done in a poofteenth of a second compared with a simple throttle closure?