From perldiag:

       Can't use "my %s" in sort comparison
           (F) The global variables $a and $b are reserved for sort co
+mpar-
           isons.  You mentioned $a or $b in the same line as the <=> 
+or cmp
           operator, and the variable had earlier been declared as a l
+exical
           variable.  Either qualify the sort variable with the packag
+e name,
           or rename the lexical variable.
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This is why variable names of $a and $b are highly discouraged -- even when they are lexical, they can still indirectly interfere with sorting. Even when you split out the sorting subroutine, the variable names $a and/or $b are still bound to lexicals, not the global $a and $b (Perl just doesn't complain in this case). Thus the sort comparison returns the same thing every time, and your list still doesn't get sorted.