It's specifically an addon for folks who normally have dozens (or hundreds) of tabs open, and I can only imagine it's actively detrimental to someone who only has a handful of tabs at a time.
IMO you should just be thankful that your workflow/habits haven't develop in such a way that you benefit from the organizational power of tree style tabs ;-P
I'm a zillion tab person. But even aside from that, it improves the usability of the browser.
A problem with browser UI is that - given our monitor form factor - it makes text hard to read. Studies show that very wide columns of text are harder to read than something relatively narrower.
By changing the viewing pane of the browser, moving the tabs off the top and to the side, we mitigate that extra-wide shape somewhat, making the text more easily readable while giving ourselves a bit more vertical space.
You can make it look better by giving FF a dark theme. I agree it doesn't look great out of the box.
As for the use case, I don't think it's an understatement to say it changed how I browse the web. Before I discovered Tree Style Tabs, I was like you -- I only kept a few tabs open and was diligent about maintaining a coherent working set.
Now, I build hierarchical structures of nested tabs based on what I'm working on, and I easily reach the 60+ tab range on a daily basis. Instead of those tabs feeling like a burden, it's trivial to make use of all of them without feeling like anything is cluttered. I can maintain so much more organized information at my finger tips in Firefox than I ever could before.
Does it reduce memory because it's more like a temporary bookmark system?
Why does it look so ugly :(