As all 4 of my children have proven many times, any 6 year old can fly an airplane straight and level at cruise. It's when you slow down and start turning that it gets interesting.
That happens mostly on approach and landing, but also on a turning departure, which is also where most accidents happen. That's exactly where I've found the AOA most useful.
In a light airplane that has an AOA, I almost never even look at the airspeed when turning base and final, I'm looking at my aim point on the runway, looking for traffic on long final (uncontrolled airport) and I'm cross checking the AOA as I slow and configure.
In a light G/A aircraft (any single engine prop) you can pretty much feel when you are getting too slow/too high AOA, as the elevator gets heavier in the turn.
I once delivered a Piper Cub from PA to FL with no airspeed indicator, due to water in the system. 6 landings with no airspeed indication, but in a Cub, the AOA indicator is the open door, when it lifts up, you need to unload it!
It's the larger/heavier jets with no real feedback through the flight control system that can benefit most with an AOA. I don't know how you guys were first taught to fly, but my IP never mentioned airspeed in my early lessons, he mentioned "Feel", as in, "Feel that? It's sinking!"
When I go out in a new (to me) airplane, one that I've never flown before, usually solo, I fist go out and practice slow flight. Not all the way to a full stall, but just close enough to get the feel of it when it's slow.
Once you develop the feel, you really don't need an airspeed indicator for pattern work. You'd be much better off to keep your eyes outside, looking for traffic if you are at an uncontrolled field on any weekend!