Wordpress - Getting the IDs of a custom post type

You can get a simple array of CPT IDs by using get_posts with the fields parameter.

$all_post_ids = get_posts(array(
    'fields'          => 'ids',
    'posts_per_page'  => -1,
    'post_type' => 'case_studies'
));

Found the basis of the answer buried in the codex

$args = array( 'post_type' => 'case_studies');

$loop = new WP_Query( $args );
while ( $loop->have_posts() ) : $loop->the_post();
    the_ID();
endwhile;