Tests fossilize a design. This is generally a good thing and allow you to focus on refactoring and bug fixes with some confidence that you won't break anything. It's also especially good for products that must adhere to specific interface or API.
But when you want to re-write the last thing you want is to fossilize your design. You explicitly don't want the same system you started with otherwise it wouldn't be a rewrite, It would be a refactoring.