After reading the Doc(tm), I think there is still design space to explore. For most readers, and many authors, keeping track of the points in an argument is actually pretty hard mental work. Just a little help would make them be better at it.
The trick would be to create "just enough" structure that is easy to fold into the process of authoring a long post or writing a quick comment. I don't think we need to reproduce all the elements of formal analysis here (and if we tried, it would be unusable).
In the end, I might argue myself back into the model where there are just "claims", not "claims" and "evidence".