Whatever the merits and demerits of downshifting an auto, I must clarify the misconception that high engine revs on a closed throttle use fuel.

Release the throttle = switch off the injectors, as can be seen by watching your fuel flow meter for those with trip computers.

I take the point about heat going into the box, but engine braking is a recognised form of slowdown, so auto box designers I'm sure allow for it in the design - if not, you wouldn't be able to override the downshifts in any way.