add_post_type_support but for front_page only

If you want to enable excerpt for specific page, then you can add some conditions to narrow down.

For check “front page id” you can use get_option('page_on_front'); in admin area. (is_front_page() should not work here)

global $pagenow;
// check current screen is edit page 
if ( $pagenow == 'post.php' ) {
    $fron_page_id = get_option('page_on_front');
    $current_page = $_GET['post'];
    // check current page is match with front page
    if($fron_page_id == $current_page){
        add_post_type_support('page','excerpt');
    }
}