You need N joules to heat up the 300kg of the engine. It doesn't matter if you sit there for 15 minutes freezing your ass with an engine running at 1500rpm (and all other car parts still freezing) or 5 minutes actually driving at 3000rpm - you still spent N joules on heating, difference is the time. And the car heater runs on the engine heat, not on the electricity, so the sooner you would warm the engine the sooner your car interior start to warm and stops seeping the heat from engine.
It's actually more importantly to have enough viscosity in ATF, but again, the sooner you would go the sooner it would warm.
For the good of the engine maybe. For the good of the driver... when you're finished scraping off it's better inside. Plus the windows kinda warmed up so it's easier to scrape.
Depends on the weather. There were a multiple times when the running engine heating up the windshield was the necessary prerequisite to scrape the ice off.
I've definitely had a serious enough layer of ice on the windshield that my nice scraper was an exercise in futility. Maybe 2-3 times a year, but it's a thing.
> I’m curious about that recommendation, do you know why that is?
I was always told (since the 90s, anyway) that it's better to drive off slowly with a cold engine and let all the components come up to operating temperature together than to drive off with a hot engine, and cold gearbox, driveshafts, tyres, etc.
I generally let a cold engine (i.e. overnight) idle for maybe 30s before driving off slowly, and it reaches operating temperature in about 5m or less.
It's actually more importantly to have enough viscosity in ATF, but again, the sooner you would go the sooner it would warm.