Maybe I am not understanding what term_order is for. And I see now that it is used in more than one table. I’m talking about the one in wp_term_relationships.
For example, in this table you could have multiple posts (represented by object_id) tagged with taxonomy_term_id 3 and could these not be ordered 1,2,3,4,5,6, etc. using the term_order in that table?
Think of it like this: I want to make a list of top 10 news stories from 2005 in a specific order. I create the tag “Top 10 from 2005” and tag posts with that, but how do I ensure that I can display these posts in a certain order?