One reason I haven't seen mentioned yet in this thread is that even for modern turbo diesels you are instructed in the owner's manual to let it cool for about 4-5minutes before shutoff. IIRC this allows the turbo to cool enough to not get damaged when there's no airflow. Funny enough they also tell you not to let it run too long, presumably because the engine is too cool to burn it completely and you get residue buildup; I believe this is due to the biodiesel they cut most fuel (diesel #2) with.

Source: I own a modern turbo diesel and read the manual.

For diesel, there is the thinking that if you keep the engine idling rather than turning it off and back on (letting it cool down) it will last much longer. I don't know how much truth there is in that but I do know it is a popular opinion.

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.

Yeah. I have a diesel made in the 70s and it amazingly still runs, and starts in the winter without glowplugs. They are amazing things.

Do you turn your car off when you are waiting outside a house to pick someone up? Most people don't. They just aren't thinking about it.

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

Maybe you want the radio going? Maybe you want your music to stay on? Lots of reasons people would unthinkingly not do this. My goal was to point out that for many this is an unconscious decision.

You don't need the engine running to have the radio going. In my experience, most people turn off the engine and leave the radio on while they're stopped briefly. It's why the ignition keyhole has an ACC position.

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

Neither are needed 95%+ of the time when the time period is waiting for someone outside their house.

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.