Custom user profile displays
I would suggest that following best practices this should definitely not be accomplished by modifying template files. If you change your theme for example, this functionality should not be effected.

A custom module would be a better place to accomplish this using hook_user_view() http://api.drupal.org/api/drupal/modules!user!user.api.php/function/hook_user_view/7 and modify $account->content to drop the fields that should not be displayed.