If people knew how to drive efficiently they'd use gears to do this and only use brakes to stop. Just sayin'
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.
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).
For what it's worth, it does makes complete sense to leave the car in gear while braking and not to change to neutral.
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.
When you need to go from 50mph to 30mph you dont need brakes at all.
Just saying / rant over / other clichéd sign off.
I think it's called Deceleration Fuel Cut-Off (DFCO).