You’re not putting any extra strain on the engine, but you might be putting extra wear on the transmission.
You’re trying to save inexpensive brakes by using a very expensive transmission. I don’t see the logic.
I generally get 50K miles out of my brakes, and I never downshift (manual or automatic) as a means to slow down.
Brakes are for slowing. Drive train is for going.
I agree with downshifting on long downhill sections, to avoid too much speed, but I can’t see doing it every day under normal driving conditions.
It is, however, your car, so you can drive it as you see fit.