Wordpress - How to remove categories filter from wordpress admin?

I tested this and it works for removing the categories dropdown on the All Posts page:

add_action( 'load-edit.php', 'no_category_dropdown' );
function no_category_dropdown() {
    add_filter( 'wp_dropdown_cats', '__return_false' );
}

-- below: old answer when I misunderstood the question --

The code you posted works just fine for me. But here's an alternative you might try:

add_filter("manage_posts_columns", "my_post_edit_columns" );
function my_post_edit_columns($columns){
    unset($columns['categories']);
    return $columns;
}

This will also impact other post types that have a 'categories' column.