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.
Every engine will start to choke when demand torque from the transmission, or better said from the tires, gets close to the engine's output torque at that state, RPM, breathing, engine capacity to shed the heat, and many other factors.

All engines need a burst of torque to accelerate their angular speed and that torque comes from the gap between available and demand torque.

A good driver or a good automatic transmission will keep the demand torque under available torque to let the engine breathe and rev up and deliver the best performance till the RPM nears the maximum engine's design RPM and available torque is so much more than the demand torque that will allow up-shifting for speed without choking.

And then and only then what you mean to say (if I understand correctly) is applied, higher gears are engaged or even overdrive.