I've done a few rewrites, in all cases they were projects that were written entirely by junior developers (company took a while to learn the costs of cheap developers) and with absolutely no tests whatsoever.

If you're rewriting a project then you're probably going to have to bin the unit tests. If you're rewriting it's because you want to make some drastic structural changes and unit tests are just too tightly coupled. Integation tests on the other hand can be an absolute godsend, you can swap out the entire stack and they'll still provide just as much value as before.