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.