I don't know. Tests freeze design so if you make your tests too comprehensive you'll just rebuild the existing system. This might be the correct approach if you are changing platforms/languages but often what you want is a system that is actually fundamentally different from the one you started with.
I would agree if I were considering unit tests, where the implementation details fall into testing scope, but I was deliberate in my word choice.
Integration tests exercise behavior at the boundary of the system under test, where it integrates with other systems, which is ultimately what you want for steering a rewrite.
Thats probably not a bad thing if it's behavior that is frozen. I find the most successful rewrites change as little as possible and iterate gradually while the least successful rewrites try to be a mix bag of everyone's wishlists.
