A mixture cut <snip> gives indications that more closely resemble a real engine failure in a normally aspirated aircraft. In other words the manifold pressure and RPM indications mimic a real engine failure.
Closing the throttle gives a false manifold pressure indication and the throttle lever is in the wrong place for the drills that need to take place.
I've never had an issue bringing the power up from mixture cut.
Correct and unsurprising, although in some cases the resumption of power may depend on the specific fuel system fitted to the particular engine and aircraft.
But I have the popcorn ready for this one:
A mixture cut is kinder in the engine pistons and rings ...
Pray tell us your theories around this assertion.