Turns out \2 or \g{-1} is not the point here, while the latter is far more stable when refactoring.

Consider this input: "abbcca"

Your recursive approach without an outer loop will produce "aa" while the solution is ""

This might (rather not) be a solution without loops.

  $s =~ s/
       (
         (
           (.) \g{-1} 
         )+
       |
           (.) (?1) \g{-1}
       )
     //xg;
[download]

Frankly I don't know, it's only passing all the tests so far.

Regarding your performance question: the recursive search does a horrible amount of backtracking trying to find a match.

Because every single character allows you to descend further and further, and with longer strings it'll take a while till you mostly don't find the counterpart, and have to track back.

Try to insert various (?{perl snippets}) in your regex and you'll see how many useless branches are searched.

At the same time the original algorithm just needs to compare to neighboring letters, and is hence far faster.