The nath package with \delimgrowth=1 is very close to your preferred style.
\documentclass{article}
\usepackage{amssymb}
\usepackage{nath}
\delimgrowth=1
\begin{document}
\begin{equation}
1 - (1-F(x))^n \\
\Pr(X_{(1)} \le x) \\
\mathbb{E}[\min\{X_1, X_2\} ] \\
( \pi - \arccos (\frac {y}{r}) )
\end{equation}
\end{document}
Read the nath guide for details, especially the part about incompatibility with amsmath.
Option 1: sed
The stream editing tool, sed, would be a natural first choice, but the problem is that sed can't match non-greedy regular expressions.
We need a non-greedy regular expression here- to clarify why, let's consider
sed -r 's/|(.*)|/\\abs{\1}/g' myfile.tex
If we apply this substitution to a file that contains something like
$|a|+|b|\geq|a+b|$
then we'll get
$\abs{a|+|b|\geq|a+b}$
which is clearly not what we want- regular expression matches like this are greedy by default.
To make it non-greedy, we typically use .*?, but the problem is that sed does not support this type of match. Happily (thanks Hendrik) we can use the following instead
sed -r 's/\|([^|]*)\|/\\abs{\1}/g' myfile.tex
Once you're comfortable that it does what you want, you can use
sed -ri.bak 's/\|([^|]*)\|/\\abs{\1}/g' myfile.tex
which will overwrite each file, and make a back up first, myfile.tex.bak
Option 2: perl
We could, instead, use a little perl one-liner:
perl -pe 's/\|(.*?)\|/\\abs{\1}/g' myfile.tex
When you're sure that you trust it is working correctly, you can use the following to overwrite myfile.tex
perl -pi -e 's/\|(.*?)\|/\\abs{\1}/g' myfile.tex
You can replace myfile.tex with, for example, *.tex to operate on all the .tex files in the current working directory.
Details of perl's switches are discussed here (for example): http://perldoc.perl.org/perlrun.html#Command-Switches
Best Answer
TeX also offers a primitive parameter to always make delimiters grow.
gives the desired output.
\delimitershortfallis meant to measure how much larger the content is allowed to get before the delimiters start growing, but by setting it to a negative value delimiters always grow.