What Yeager meant by that comment was that he feels AOA through buffet on the aircraft. IE in a turning fight, he's not looking at gauges, he's feeling the aircraft's response to his pull. What's a mooney feel like to you when you're pulling for a guns track?
Why do most pilots fly airspeed on the board? Simple: they don't have an AOA probe and they are comfortable with flying a sloppy approach. They'd rather have a 10k aspen that provides no new info (just a fancy glass display) than an instrument that costs $800 and can show you A) max efficiency for your airfoil and your stall margin at any time. Airspeed is a "comfortable" gauge for those used to driving cars... One problem though: your wing stalls at different speeds, depending on weight and in a way, angle of bank. Even your best calculated approach speed is not going to be the exact number (weight and balance is off, math is off, etc etc). You fly exactly 72 mph every landing? Based on what? Your factory weight and balance plus estimates of your baggage and weight? Even if you could hold that exact approach speed you calculated, your number is probably not percise. AOA is the truth data, because your wing stalls at a given AOA every time, regardless of weight, angle of bank, or anything else.
When landing you can fly by airspeed, calculating your gross weight and coming up with an estimate of what you think is your final approach speed, or you can go straight to the truth data on how your airfoil is performing: AOA.
AOA approaches and landings are the going in answer in both the F-15 and F-18. No good reason why they shouldn't be in a mooney or any other aircraft either (other than the fact you don't have a stock gauge).
Then again, what do I know... I've only landed on a moving carrier deck 355 times...