My main argument against mixture cuts is that (especially for turbocharged engines) its not a very kind thing for the engine. There is no need for the simulated power loss to be total & sudden. Its unlikely to occur in a black & white sense like that in real life. A gradual power reduction using throttle then simulating zero thrust instead of feathering is much more kind to the cylinder heads.
As for low level training - one of the best learning experiences I've had was a simulated engine failure at about 50 ft. I don't think it needs to be part of the recurrent training regime, but as a one off experience as part of the multi endorsement it was gold. However, the caveat is that it was a country airport with no traffic and flat paddocks in front of us. It has no place in any other environment. I couldn't tell you how the instructor did the cut. I was fully absorbed with other activities. And he never restored the power. We climbed up to circuit height at about 100 fpm. The flying precision required is indelibly etched in my mind. I don't think you'd learn the lesson any other way.
Each month when I do a sim session I cut an engine (I use mixture here!). Typically midway in an instrument procedure. But here I think the main point of the training is memory reinforcement of the checks and making the initial actions automatic. Whatever SIM the club has does a reasonable job of simulating asymmetric trust.