There is another down side to leaving the car idling for a long time, particularly if all the electrical consumers are going full chat.
You are placing the greatest demand on the electrical system right when it is least able to satisfy it.
By that I mean that the battery is very cold, so it cannot give the same current to the system as in the heat of summer, plus the alternator is only spinning at idle revs, so will not be capable of supplying full capacity to offset the demand places upon it. So the electrical system is given a very hard time as a result.
Of course if you drive off straight away, the charging system can supply full capacity because the alternator will be spinning at higher revs.
Plus you give the engine some work to do, so it warms up much quicker.
Win win.