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I am an older person, been driving for 50+years.
From the "old school" whenever driving continuously downhill or in stop start traffic, my preference is to use a lower gear to help control the vehicle and to reduce excessive demand on the brakes. I certainly feel more comfortable with some engine braking where appropriate - and it avoids snapping passenger's heads backward and forward.
I have picked up some comment (from somewhere?) that suggests, for maintenance cost reasons, you should use the brakes rather than the gearbox.
I am generally driving auto now. Comments please.

Most modern automatics with intelligent electronic management systems automatically detect over-run and so ensure the vehicle is in the appropriate gear when going down hill, so on that basis, only light braking may be required.
It is not recommended to shift the gear lever into a lower gear under normal driving conditions, as this will result in wear in the clutch packs in the automatic transmission. Obviously, there may be some extreme situations (perhaps snow and ice or loose gravel etc, where you may wish to have more engine braking at low speeds etc), where manually using the gears may be advantagous, but it is the exception rather than the rule.
Being mindful that a set of brake pads is far cheaper than a transmission overhaul, these days we'd advise light braking application under most conditions as opposed to chopping between gears.
I trust this explains the comments you've heard elsewhere, which we would agree with.