You're right but the vast majority of the time the difference between the AI and the AOA is close to zero (plus whatever the angle of the wing is relative to the fuselage which is fixed and should be pretty small anyway). The times when the difference between the AOA and the AI is very different than zero in a bad way the little stall switch on the wing and some sort of chime/buzzer will be more than happy to let the pilot know.
My point is that the AI combined with the little stall switch on the wing seem to be good enough for the overwhelming majority of cases. Add in airspeed and you're more than covered.
We keep trying to add systems to cover whatever remaining edge cases we find but those systems have failure modes too so we take three steps forward and two steps back. These systems pick up the slack when the pilot might be inattentive but the increased complexity and cognitive load poses other risks.
Loss of control during approach and landing because of poor airspeed control kills pilots every year. It's important enough that the EAA has a dedicated "loss of control initiative" to try to figure out what to do. See for example https://www.eaa.org/eaa/news-and-publications/eaa-news-and-a...
Climbs after takeoff are a situation where they will significantly differ, and also one of the times when this information is more important.
Attitude indicator? Look out the window! Stall horn? Just feel the pre-stall rumbling through the controls. You can fly a plane with no instruments. None of them are strictly necessary, but it’s a good idea to have them.
Or consider an aerobatic airplane at the first vertical point in a loop. The airplane's pitch is 90° but the angle of attack is less than 10°.