# Why polynomial interpolation is considered as better than others?

Why polynomial interpolation is considered as better than others?

In case of interpolation, the function $\phi(x)$ to approximate the unknown function $f(x)$ may be polynomial, exponential, trigonometric sum, Taylor's series, piece-wise polynomial etc. Then why polynomial interpolation is considered as better than others (although I know that there is a justification for approximation by polynomials (Weierstrass's theorem), but it does not true that there is no justification to approximate by exponential, trigonometric etc).

Some where I read, reason for considering the polynomials in the approximation of functions $f(x)$ is that the derivative and indefinite integral of a polynomial are easy to determine and are also polynomials. But if $\phi(x)$ is exponential, trigonometric sum, Taylor's series, piece-wise polynomial etc then also derivative and indefinite integral are determined like polynomials.

Then what are other reason(s) for taking polynomials into consideration?