Display Taxonomies in loop with template args

The simplest solution:

echo get_the_category_list( ', ' );

Following your way:

Change your $args like so:

$args = array(
        'template' => '%2$l',
        'term_template' => '%2$s',
); 

And then, add this to your functions.php file (this will affect all %l markers!);

add_filter( 'wp_sprintf_l', function($templates) {  
    // $templates['between_last_two'] = sprintf( __('%s, and %s'), '', '' );
    // $templates['between_only_two'] = sprintf( __('%s and %s'), '', '' );

    $templates['between_last_two'] = sprintf( '%s, %s', '', '' );
    $templates['between_only_two'] = sprintf( '%s, %s', '', '' );

    return $templates;
});