Engine braking wears transmission components which are considerably more fragile and expensive than replacing brakes. Engine braking only stops you using the driven wheels, brake discs apply to all wheels.
No it doesn't. Synchronized, rev-matched downshifts put negligible load on the drivetrain. Coasting to a stop with the gear already selected, putting it in neutral just before stall does that even less. The stresses produced by acceleration are ballpark estimate around an order of magnitude greater. This can be inferred by the fact that usually the rate of deceleration by engine braking is smaller than the rate of acceleration for a given gear ratio, ergo, the drivetrain is strained less.
It still wear components that are not as easily replacable as brakes. As for coasting to a stop whilst still in gear, I agree with that being a good idea but I don't think that's what digitalWestie was getting at.
Engine braking allows you to save fuel (by using stored energy of the drivetrain to handle compression of the air that normally would require work from combustion).
And, as long as the car remains in gear there's not much extra wear on the transmission itself (certainly not compared to the torque from the acceleration the preceded it, at least).
I think we're talking about different things. digitalWestie's advice to use the gears to slow implied changing down through the gears to use the engine to brake, not simply leaving the car in gear while applying the brakes.
For what it's worth, it does makes complete sense to leave the car in gear while braking and not to change to neutral.
Engine braking wears transmission components which are considerably more fragile and expensive than replacing brakes. Engine braking only stops you using the driven wheels, brake discs apply to all wheels.