Implying that it's more convenient/easier/quicker to leave the aircraft running versus shut down/restart puzzle me. My experience is exactly the opposite, at least single engine. Sounds a bit puritanical to me.
Perhaps a couple decades in the Rubber Ducky, also known as the AS350, have hazed my recollection. Lock the collective, tighten the cyclic friction, do the interminable paper work, and enjoy the heated/cooled air staying dry. It's short-coupled stiff legged beast, so the skids might shift, but I'm sitting at the controls.
Versus double checking how the aircraft sits, locking the collective, leveling the disk, applying sufficient twist on the cyclic friction that I'm positive it isn't moving (the French must be very supple with clamp-like grips), sliding the seat back, undoing my harness, unfolding from the seat to exit, watching the tail rotor like a hawk as I walk about- pilots have walked into their own TR- and doing my ground recon (Yes, LRP, I remember). Then reverse the process. The cyclic friction knob is always more difficult when decreasing friction.
The ground recon in and of itself justifies the work, especially at night. I don't lay rocks and chips, but I do carry an intense 'torch' (flashlight) to scan the immediate overhead for wires, the ground itself for less obvious hazards (fire ant mounds are also a real problem for my crew), and then the perimeter skyline for occult wires. Company policy is that I not use a hazardous LZ, but the high/low recon are conducted in high workload situations, ad the ground crew's preparatory evaluation is done by, well- amateurs.
Helicopters go where it's less efficient for ground transport. There are very real risks in shutting down/restarting: batteries, starter generators, relays, etc. I might opt to leave the pig running instead of discovering a start maintenance fault 3 hours by ground from pavement, or even more embarrassing- on a major traffic artery. If everything works, I can start before the nurse closes the medic door, walks around and buckles in. It's much easier to do that.