Why don't we consider pressure as the driving agency for motion, instead of force, because the force applied is on an area/part of the body only?

Because it's a lot easier to work with. You could use pressure to calculate how an object will move/behave but you would have to work out the average pressure acting on the body and multiply it by the surface area which would give you the force anyway.

It is similar to how we model gravity to be acting on an object's center of mass even though in reality it is acting on every atom in the object separately