It seems like an oversight that this feature has never been added, there's no plugin or (easy) code solution that I've found, and it can cause usability issues without it being there.
On the third point, here's where a problem arises:
- You have multiple custom post types. Let's call them Art and Science.
- Both of these custom post types have registered tag or category taxonomies: art-tags and science-tags.
- Both art-tags and science-tags have a tag called "Canada," but for them to work properly, they MUST have different slugs, like canadian-art and canadian-science. If you try to add "canada" to both art-tags and science-tags on the category/tag pages, the second time you add it, you'll get an error: "The slug 'canada' is already in use by another term"
- If you add these via the tag/category pages, making a custom slug is easy, but if you add a tag that shares the same term with another post type's tag via one of the editor pages, you don't have the option to edit the slug immediately. In WP, what happens is, say you've got art-tags/canada already, if you add your Science post to a new tag called Canada, it doesn't go to science-tags/canada. It goes to art-tags/canada, the preexisting term and slug.
This is really, really annoying if you're dealing with lots of post types and tags. It means you have to remember to stay on top of any new categories or tags. You can't just create content; you also have to keep returning to the tag/category pages.