permalinks issue and archives

Now the question is why does WP only put the word “date” in when the permalink is “/%post_id%/%postname%/”?

Because the WP_Rewrite class method get_date_permastruct only looks specifically for a clash between %date% and %post_id% tags.

To get this date structure with other numeric-based post permalink structures, you can manipulate the date structure directly:

function wpa57228_date_structure() {
    global $wp_rewrite;
    $wp_rewrite->date_structure = $wp_rewrite->front . 'date/%year%/%monthnum%/%day%';
}
add_action( 'init', 'wpa57228_date_structure' );