As part of our rewiring project, there are some old romex runs that
are no longer needed.

The wire is difficult to pull out, presumably because it is stapled to
the studs.

Is there any trick (other than adding more brute force or opening up
the wall) to pulling the wire through the staples and out of the wall?

Thanks!
-----------
It's not necessary to remove the old wire. You can safely abandon it
in place.