Old aliases / permalinks are kept and redirected to the current permalink, which is wonderful. For retention of search engine links and other referrals, this is crucial when users change the permalink field. However, there is a huge part missing.
What happens when someone changes their site architecture? What about when someone switches to WordPress and needs old URLs to point to the correct pages in the fancy new WP URL structure? This needs to be addressed in a big way.
Not only should 'backed up' aliases / permalinks be shown and modifiable on the edit page, but there should be a settings page for viewing all or performing bulk actions on permalinks. This has probably been avoided because it's dangerous to give that much power to users. However, if only the 'backed up' aliases are shown in this settings page, then the current site permalinks would be safe at least.
The most important feature of this settings page, in my opinion, is the ability to quickly add aliases and assign them to pages/posts in the current site. This way redirection for all the 'old' URLs can be quickly set up when making major changes, like moving to WP and updating URL structure.
I forgot to mention .htaccess. Thanks to Mika for reminding me in the comments.
WordPress is all about being simple to use and as powerful as possible, right out of the box. Requiring this functionality be handled by modifying the .htaccess or by other means through server settings is cruel. This is a big enough issue for many people who are moving their site over to WP for it to be included as a core feature and not a hole to be filled by plugins (at least not in its most basic state).