Originally Posted by werbil
...I suspect the reason they keep the engine running in this case is to reduce the number of cycles on the engine...
That is a good thought, but I believe (I am not 100% certain of this, but reasonably certain) that each takeoff and landing is counted as an engine cycle for the purpose of calculating component life, regardless of whether or not the engine was left running or shut down.
I recall seeing a service letter that P&W Canada circulated about 20 years ago in which they provided a formula for operators to use when they were making frequent short flights without shutting down the engine. Whether this formula affected TBO or just certain cycle-limited components (e.g. turbine wheels) I cannot recall.