Is there a plugin that will completely remove the category system?

Why hack apart what’s already there? If you remove the built in taxonomies, you’ll end up creating hiccups in core code that expect them to be there!

You’re much better off just editing your theme file(s), or filtering out categories on the front-end (ask if you need help on that).

For example, in your theme’s index.php and single.php, you might have something like;

filed under: <?php the_category( ', ' ); ?>.

Just remove it and you’re done!