Funny story, I had almost exactly the same idea in 2013 and prototyped it in Mathematica (probably a lot of people have had this idea). Here's a screenshot of some random thread that I happened to visualize (comments were visible as tooltips in my rough and ready implementation): https://imgur.com/a/9xfw6cA (color represents common authorship, size is comment length). I didn't have the Javascript chops to do anything usable, let alone as polished as the linked Chrome plugin; kudos to the author!

Another thing I was doing at the time was visualizing Twitter and Facebook friend graphs, and the first insight there was to deliberately drop the 'ego' node, as it destroys any hope of effectively showing community structure of the friends themselves (it also carries no extra information as everyone is necessarily connected to the ego).

So perhaps a similar thing would be effective for threaded conversations: if you drop the root node, disconnected discussions will become separate trees in the visualization, which will help with efficient use of space, and the tail of singleton comments that no one replied to will become isolated disks that can space-fill the background. Switching to an actual rectangular tree layout as I used in my prototype will also help in that one consistent direction (down) represents nested depth.