Parallel_enable PL/SQL function doesn't run in parallel

Question

I have a pl/sql parallel_enable pipelined function to write files. The select statement with the parallel hint runs fine in parallel if running separately. But the function doesn't run in parallel. Anyone knows how to fix it?

select *
  from table(parallel_x(cursor (select /*+ parallel(c, 5) */
                      c.cid
                       from customers c)));

create or replace type x_t as object
(
  line_count number,
  session_id number
);

create or replace type x_tab as table of x_t;

function parallel_x(s in sys_refcursor) return x_tab
  pipelined
  parallel_enable(partition s by any) is

  session_id number;
  f          utl_file.file_type;
  line       varchar2(32767);
  line_count number := 0;

begin
  select sid into session_id from v$mystat where rownum = 1;

  file_name := 'file_' || session_id;

  f := utl_file.fopen(location     => 'directory',
                  filename     => file_name,
                  open_mode    => 'w',
                  max_linesize => 32767);

  loop
fetch s
  into line;

    utl_file.put_line(file => f, buffer => line);

line_count := line_count + 1;

exit when s%notfound;
  end loop;

utl_file.fclose(f);

 pipe row(x_t(line_count, session_id));

 return;
end;