I came accross this thread thinking of CodeIgniter with WordPress on top.
For those wondering what the use would be, personally I think that as much as WordPress rocks as a platform, the underlying core of WordPress sucks in terms of design pattern. And CodeIgniter I think has a great design pattern, which is MVC with some nicely separated libraries and helpers.
So to me, working out how to convert the WordPress core into a CodeIgniter application could be very interesting, albeit pretty time consuming. The WordPress CMS, The Loop and everything would still be there, just sitting on top of a proper MVC framework. WordPress 4 anyone?