Salute!
Thank you Fortissimo.
To be honest, we fighter guys never used AoA to fly the 'quickest, tightest turn", or to hang at best AoA as MIGCAP, or to cruise home or let down at optimum AoA.
We used it mostly for approach and landing. And as you said, the absolute AoA was not necessary. What the U.S. Navy and later USAF presented on the modern HUD and "indexer" chevrons on each side of the old gunsites was where you had to go to reach and fly optimum approach AoA. I liked it.
So your idea of having AoA represented in some fashion once gear is down, maybe when flaps are down and gear coming up as for a go around has merit, IM(not so) HO.
Gums sends...