Checked it numerous times, saves a minute or two, sometimes more:
Limit and control the number of people approaching and departing the aircraft. PIC can be part of that if you're shutdown. Otherwise you're sitting there watching and communicating with handsigns... if.
Easier to deal with sheets, blankets, ball caps, paperwork, etc. when shut down.
Better ground recon.
One is more likely to have maintenance issues arise in the restart. Classic example in an Astar and single engine Bell- starter/generator won't turn. You have no way of checking that before the shutdown, and you're toast until maintenace arrives. In the wayback times (maybe offshore, maybe not) one could "malletize" the st/gen., perhaps knocking a stuck brush loose and start the pig.
As stated, clear traffic lanes if you can, don't shut down in inaccessible areas, etc. But if your business is patient care, time matters, and it is quicker to cold load and restart. Some requesting agencies don't buy it, they want to think you're gonna grab and go...