I suspect the reason they keep the engine running in this case is to reduce the number of cycles on the engine - and subsequently the long term maintenance costs. It is my understanding that some of the engine components in the PT6 are life limited by cycles which include both a take off and an engine start. Cut out the start and it reduces the number of cycles.
With the PT6 114A, typical ITT temps we see in our operation are 660oC idle, 780oC peak start, 720oC take off, 680oC cruise - each engine has its own characteristics. After a short shut down, the ITT indicates about 250oC with no air moving through the engine. The temperature differences between idle, take off and cruise (typically 60oC variation) are much less than those involved in starting a hot engine (typically 500oC variation). Whilst the metal has thermal mass and doesn't change temperature instantly, significant thermal stresses occur during start and shutdown that don't otherwise occur. With the PT6, it is very important to shut down from a constant, stable temperature (min 1 minute) otherwise tips of the turbine blades can rub.
Other components, especially the battery and the starter/generator also work hard during every start.