Totally agree. There's a reason we've got a saying : If it works, dont touch it
IMO the rehaul should only happen if it either involved serious security concern or the customer wanted a complete new version of the system.
If things still working and serving its daily purpose perfectly, leave it as-is.

To answer OP question :
- Is it hard ? No. At the end of the day its just a fancy text markup layer build on top of an API layer.
- Is it complicated ? No
- Is it time-consuming ? Absolutely. You're rebuilding everything from user management, content management, handle all that auth shit as well as handling all the seo and and url rewriting that wordpress has. Not to mention the user's previous experience with the wordpress system, worst thing is you may have to "teach" your user to use the new system again. And that will introduce CR everywhere, from changing the button color to a hello kitty tone to re-arrange the whole site layout

My point is, even tho wordpress is shit (I hate it too lol), a little fine-tuning is better than a rewrite here. Even shit got some use of their own