Timothy, you are exactly right and I congratulate you. The American Aviation AA-1 Yankee and AA-1A Trainer built first until 1978 before successor company G-A bought the designs on that Approved Type Certificate have a combination of high induced drag and low longitudinal stability at takeoff and landing speeds. Their blunt, short form sinks rapidly and controls are twitchy at lower speeds. Short wingspan and boxy fuselages give induced drag and the poor stability is due to small tail size and short fuselages. Landing approach requires 70 knots with flaps, 75 knots clean or 65 knots with power. Things happen fast. Crosswinds complicate things.
They tend to go flat in a spin and can't be recovered if in a flat spin. Therefore, they are NOT certified for spinning and have a poor safety record, higher than any other single-engine aircraft then in production. If rudder and aileron coordination is poor on base leg and final-a skid will result in a quick spin, not good at these altitudes above ground
The construction chosen tends to cause the problem. The rigid bonded honeycomb has thicker un-tapered sections than need be and a strong tubular spar un-tapered toward wing tips has too much weight outboard. Economies of production of a boxy fuselage, etc triumphed over aerodynamic design.
If someone buys these aircraft intending to learn to fly with them, their instructor should teach approach to spin training in a different, more benign trainer aircraft, my opinion. Our FAA probably learned some lessons also about certification requirements from the accident history of them. Some of my sources of this are from owner comments.