Two points wrong, one crucial!

1) Shifting from N->D while moving will NOT damage the auto tranny. The torque converter gives the engine time to rev up until it matches the wheel's turning speed. The effect is just the same as on a manual car if you shift from neutral into gear when moving: release the clutch slowly and engine rev slowly goes up; release the clutch too fast and you feel the drivetrain shake a bit, but it won't be damaged. Of course you don't want to do this every day, and there is no need to; but the physics is that doing it by mistake once or twice won't break things.

2) Of course there are times you need to use engine braking! If you descend from a high, steep mountain and don't do engine braking, your brake pads will heat up very quickly, and after 15, 30 minutes you won't have any braking power at all! The effect is called "fading". Your brakes may return after they cool down, but while they are fading, it's an accident waiting to happen. So you would rather be in 2nd gear "accelerating" downhill than be in 5th grear braking downhill.