What am I doing wrong creating post draft via wp-cron? (wp_schedule_event & wp_insert_post)

The problem is that you’re only hooking the cron action on admin_init, which doesn’t run when wp-cron.php is called. So the function will never run.

So this function shouldn’t be inside wpcp_activate():

add_action( 'wpcp_cron_hook', 'wpcp_cron_do' );

Also, register_activation_hook() shouldn’t be inside the admin_init hook either.

So your code should look like this:

function wpcp_make_post( $post_title, $post_content, $post_type ) {
    $post_id = 0;

    if ( post_type_exists( $post_type ) ) :
        wp_set_current_user( 1 );

        $to_post = array(
            'post_type'     => $post_type,
            'post_status'   => 'draft',
            'post_author'   => 1,
            'post_title'    => $post_title,
            'post_content'  => $post_content,
        );

        $post_id = wp_insert_post( $to_post );
    endif;

    return $post_id;
}

function wpcp_cron_activation() {
    if ( ! wp_next_scheduled( 'wpcp_cron_hook' ) ) :
        wp_schedule_event( time() , 'hourly', 'wpcp_cron_hook' ); // = daily
    endif;
}
register_activation_hook( __FILE__, 'wpcp_cron_activation' );

function wpcp_cron_do() {
    $post_title="This should be the draft title";
    $post_content="All HERE";

    wpcp_make_post( $post_title, $post_content, 'post' );
}
add_action( 'wpcp_cron_hook', 'wpcp_cron_do' );