Cutting the engines on the ground will cause damage a lot of times. By turning the engine off you're also switching off the cooling system in most cases, since most of the oil/hydraulic/pneumatic/etc pumps in these aircraft are engine driven.
That's why it's generally advisable to keep it idling until it gets to low temperatures before shutting everything down. Most general aviation aircraft with piston engines clearly specify this in their manuals, for example "idle until temperatures drops to X degrees before shutting down".
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