They might just be travelling so often that it is just not worth the effort to remove the old tags.
In any case, are you looking at the paper tags handed out at the check-in counter rather than the status tags that "live" on bags. And why are you checking them out so closely - and isn't the written information on the inside of the folded tag?
Luggage tags can be the ones with the personal information or those for routing. I believe he meant the routing tags. However, the check-in agents should remove the old routing tags before affixing the new ones.