I don't follow you on the advantage or reason for only using the closed-over variable in one place, that being a function that returns it.

It is largely about scope management and making sure you control how many refs a given object might have. Here is some example (NOTE: I have not run this to confirm it works exactly as expected, but you should get the idea of you are familar with MooseX::Role::Parameterized)

package My::Parameterized::Role;
use MooseX::Role::Parameterized;

parameter 'something' => ( isa => 'Str' );

role {
    my $p = shift;
  
    {
         my $something = $p->param('something');
        method 'static_something' => sub {
            return $something;
        };
    }
}
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So, first let me say that this is likely overkill, but having had some nasty ref-counting leaks in the past I have learned to be cautious. So as you can see here, the 'static_something' method I am creating only closes over the $something variable, which we know is a string. If I had written 'static_something' like so:

method 'static_something' => sub {
    return $p->param('something');
};
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Then the method would close over the $p object, which *might* become a source of leaks.

Like I said, probably overkill, but I prefer to be cautious in this kind of environment.