Registering menu with 'Automatically add new top-level pages to this menu' selected

Is it possible to register a menu inside of a theme functions file and have ‘Automatically add new top-level pages to this menu’ pre-selected? I can’t find any info about this in the register_nav_menus documentation.

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That function just registers new menus.

If you want to create a custom type of menu, you need to create your own extended menu walker that would do something custom or activate any other functionality.

If you would like to have the top pages listed (in a menu or other situation), you can use wp_list_pages and limit to first level (or how many you need).