Big Pistons, I often enjoy your posts and agree with you. On this occasion I don't, because you generalise too much.
The procedures in the Grumman POH have undergone some kind of scrutiny (I wouldn't like to say how much, but they passed the FAA's tests) and they are the published procedures for the aircraft. They are the procedures by which, by law, the aircraft must be flown, and they are the procedures which, if followed, achieve the relevant safety standards.
The OP says he came in high and fast, yet he left the go-around until the last minute, it seems. That's a learning point for him. He handled the aircraft through the event without accident and probably learned about handling from that.
The AA5 is a wonderful training aircraft. Anyone can fly it, almost anyone can land it (they really made a mess of designing the nose landing gear), but a decent examiner or instructor can tell in the shortest time how skilled the student or candidate is. I loved instructing on them, and flying them myself, because flying them well requires skill.