"That also ensures that the end of the tail hook stays at the correct height in relation to the fuselage and main landing gear."
Did you fly the F8U Crusader? Variable incidence wing? Elaborate?
Could you also say then that AoA is critical at speeds approaching Stall?
No, I did not fly the F8U. My primary planes were the A-4 and the EA-6B.
At any given weight, fuselage angle is determined by AoA. If you are too cocked up, the hook will be too low and you can have a "inflight engagement" of the arresting wire. The main gear need to be on the deck at or before engagement or there will be serious damage. Essentially that means you will be pulled down instead of landing normally and then engaging the wire. Thus, you need to be on AoA or you risk an inflight engagement.
AoA is your most sensitive parameter near stall so it allows you to get closer to the optimum speed for your weight.
For carrier operations, the captain tries to keep the wind directly down the angled deck so that there is no sideslip. Landing with a sideslip is an invitation to collapsed landing gear.