It is not so much a question of smooth or turbulent air, it is a matter of the (constant) motion of the surrounding air. In a windshear situation (in a downburst) when you need it most it will have the greatest error. In calm air you do not need it.
Given the fact that any large transport aircraft does have an AoA sensor, it is just a matter of installing the indicator (or to implement the indication into your PFD). So what do you win if you calculate AoA from other data? The AoA data is there.