Query all posts in a given taxonomy

Have you tried simply omitting the 'terms' key from the 'tax_query' array?

$query03 = array( 
    'numberposts' => 5, 
    'post_type' => array(
        'video'
    ), 
    'tax_query' => array(
        array(
            'taxonomy' => 'product',
            'field' => 'slug'
        )
    ) 
);

Alternately, I wouldn’t really worry about the weight of the query. The resulting query will be what it will be, regardless of how complex the query args, or how big the query args array. So, I would recommend just pulling in all of your terms via get_terms:

<?php get_terms( $taxonomy, $args ); ?>

You can use it directly in your query args array, by setting 'fields' to 'ids', which will return an array of term IDs, rather than an array of term objects):

$query03 = array( 
    'numberposts' => 5, 
    'post_type' => array(
        'video'
    ), 
    'tax_query' => array(
        array(
            'taxonomy' => 'product',
            'field' => 'id',
            'terms' => get_terms( 'product', array( 'fields' => 'ids' ) )
        )
    ) 
);

Edit

Alternate ‘tax_query‘, using term slugs instead of IDs:

    'tax_query' => array(
        array(
            'taxonomy' => 'product',
            'field' => 'slug',
            'terms' => get_terms( 'product', array( 'fields' => 'names' ) )
        )
    )