For plain vanilla flying, D, (point to point in an M20J) what
improvement might we expect using aoa instead of what we use now in
takeoff, cruise, or landing phases?

I can appreciate aoa's utility in higher performance a/c, or maybe
when flying close to some edge, but am not sure how it would improve,
for example, our take off (best rate for the first few hundred feet,
that's less than 30 seconds of flying) , then a prudent cruise climb
to our en route altitude. En route, usually as high as possible
consistent with the trip length and winds, we go to the lowest rpm we
can, and maintain the same ias going lower until approaching the OM.