Why we use an activation function for introducing nonlinearity instead of a polynomial Perceptron implementation?
Well, thanks to the universal approximation theorem from a purely theoretical point of view, absolutely nothing.
The main issue is with computation. You can find more information here. Mainly, you want functions easy to calculate (polynomials are ok) but with specific regions where derivatives are monotonic (here polynomials are not good) and approximating the identity near the origin (again, polynomials not good).