The code snippet added to the functions.php file will remove the default WordPress widgets. I have commented the widgets I do not want to remove.

remove-default-WP-widgets.php

/* The below code removes all the default WordPress widgets. I commeted the ones I do not want to remove. */

// unregister all widgets
 function unregister_default_widgets() {
     unregister_widget('WP_Widget_Pages');
     unregister_widget('WP_Widget_Calendar');
     unregister_widget('WP_Widget_Archives');
     unregister_widget('WP_Widget_Links');
     unregister_widget('WP_Widget_Meta');
     unregister_widget('WP_Widget_Search');
  // unregister_widget('WP_Widget_Text');
     unregister_widget('WP_Widget_Categories');
  // unregister_widget('WP_Widget_Recent_Posts');
     unregister_widget('WP_Widget_Recent_Comments');
     unregister_widget('WP_Widget_RSS');
     unregister_widget('WP_Widget_Tag_Cloud');
  // unregister_widget('WP_Nav_Menu_Widget');
 }
 add_action('widgets_init', 'unregister_default_widgets', 11);