Query_vars and custom post type wp_query

Do you know why if I use this url with a variable:

https://example.com/archive-tag-and-category/?post_type=my_post_type

won’t yield any result with the following code:

$cust_post_query_var = get_query_var('post_type') ;
$query = new WP_Query( array('post_type' =>  $cust_post_query_var)) ;

whilst

$query = new WP_Query( array('post_type' => $my_post_type)) ;

works ok?

I manage to retrieve the ‘post_type’ all right but WP_Query doesn’t seem to like it…