Re: "Out of curiosity, is there a business benefit or are you doing it on your own time?"
I'm a developer, not a manager.
What you say is not universally true. It's only true if the costs of a rewrite are lower than the projected savings and if those savings actually materialise, which they frequently fail to do.
Furthermore, there's an opportunity cost - all the time you're re-writing the existing system, you're not building value.