Once, before 1990 or.so diesel engines were hard to start cold. You either left them running or plugged them into the wall so the heater instead could keep them warm. It wasn't unusual to leave a truck running all day because otherwise it wouldn't start in winter. In Russia they often built bon fires under their trucks in the morning. I know of tractors that have a gas engine just to start them, which also worked, the gas engine would run at full speed for a few minutes until the engine would finally run.

Not that the above is historical. Modern batteries are much better. Direct injection engines start almost as fast as gas engines these days.

For older diesels, it is more efficient to leave them running than turning them off and restarting them. And I am talking OLD diesel trucks that have indirect injection systems. They'll smoke a hell of a lot more than just letting them idle.

Still turn them off if you don't need it running. Most modern diesels 2004+ are way more efficient in this regard in consumer vehicles and modern diesel trucks are better than they used to be.

Yes, of course. You don't? Why not?

I would think the bigger reason is for heat/air conditioning when it is too hot or cold outside.

Probably depends on how expensive the fuel in the area is. Most people I know would certainly turn it off since leaving it idle while waiting means literal dollars worth of fuel being burned.