What's wrong with a simple vector diagram?
What's wrong with it is that it leads you into thinking that...
Lift is perpendicular to the wing chord.
...when in fact it's not. Not even when you allow for the loose terminology.
By definition, lift is perpendicular to the airflow direction, drag is parallel to it. That doesn't change with AOA. What you probably mean is that the total resultant force "is perpendicular to the wing chord". And then you want to...
Resolve that into a vertical (lift) component and a horizontal (drag) component. Higher AOA ==> more drag.
But the problem is that the total resultant force does
not simply tilt with the AoA to remain perpendicular to the chord line. If you increase the AoA, the total resultant force may change direction, but it doesn't simply tilt back by the same angle as you changed the AoA. If it did, you would have zero induced drag at zero AoA, and the induced drag to lift ratio would simply be the tangent of the AoA. It's not.