I agree with this approach and do it as well on steeper grades in my Tahoe (4L60E) if towing anything...I utilize manual shifting often when towing. It really helps going down a grade pulling over 15k. I try not to force the transmission to take the hit, I usually floor it momentarily to get the gear I want then move the shifter to that position, or Rev match a down shift. Yes, you can Rev match an automatic if you know what you're doing.
To all: Automatic transmissions that have overrun or other additional applied elements that come on when selecting a manual range setting are designed specifically to facilitate engine braking so you won't hurt the transmission if those elements are used judiciously and within their design limits.