Contrary to your opinion, \left and \right are quite rigid and unflexible: they don't provide the right size in many cases. The usual example is a summation, where
\[
\left( \sum_{k=1}^{n} x_{k} \right)
\]
produces too large delimiters. The right size in this case is obtained with
\[
\biggl(\, \sum_{k=1}^{n} x_{k} \biggr)
\]
Here's a visual comparison: left the \left-\right version; note the \, for avoiding the clash, which should also be used after \left( anyway.

This said, you're free not to follow the advice. In this case, define properly \pr and use the *-variant
\documentclass{amsart}
\usepackage{mathtools}
\DeclarePairedDelimiter{\pr}{(}{)}
\begin{document}
$\pr*{x,y}$
\end{document}
Of course in this case the parentheses don't grow, so there's no point in using \pr* instead of \pr. Here's the output of $\pr*{x,y}\quad\pr{x,y}$:

\pr*{x,y}if you want\leftand\right, after properly defining\DeclarePairedDelimiter{\pr}{(}{)}. Of course you don't need\leftand\rightin this case. And there are several reasons for not generally using them: use them only when they are really necessary, which means quite rarely. – egreg Oct 20 '15 at 13:44