I imagine that a freer flowing exhaust will cool the puppy down as well, particularly at that engine-header connection. Or at least I hope so after just performing a bafflectomy.
Lots of little things that add up to big improvements in performance and longevity.
I also performed a bafflectomy (is the word in the OED) but dont have any cooling fan. I have never noticed it go into skipfire. Being in Aberdeenshire helps, less traffic than most of England & I dont do towns very much.