Going down through the gears, so as to use "engine braking" probably dayes back to the time when the main fear was of "brake fade". City folk would rarely be troubled by this but, if you attempted a long descent in a mountainous area, you would eventually be faced with a hairpin turn, a precipitous drop and overheated brakes which no longer slowed you down.
Under those, rare, circumstances, your own life was worth more than that of a clutch or gearbox.
We have disc brakes these days, which do not suffer from 'fade' but some cheaper makes/models may have drum brakes on the rear, so prolonged braking (10 minutes plus) on a long downhill road mean you could lose a good chunk of the car's braking ability.