Question: If the car's acceleration is higher when the wheel's angular acceleration is higher(tangential acceleration=alpha x radius). Why are higher gears not used to accomplish the acceleration of the car instead of lower gears?

Answer: 
### The Rotational Inertia of individual gears doesn't matter.

You are way overestimating the effect of rotating gears on overall acceleration. The mass of gears is inconsequential compared to the weight of the vehicle (and the rest of the rotating mass. So a larger diameter first gear does have a slightly larger rotational inertia. But gear ratios overpower this small effect and renders it inconsequential.

In the end, acceleration is related to both the rotational and non-rotational mass. The small change in rotational inertia between first and second physical gears is immaterial.
You are mixed UP. The angular acceleration of the wheel does not effect the entire car's acceleration. What will, is the force applied to the ground from the tires.