This is a very anti-pragmatic way of looking at things in my opinion. The program is not a snapshot that exists in a vacuum. Most programs are going to grow over time and have things added and removed in various places by many people. They're going to have many interfaces and operations.

I think you're arguing that tests and types can both be used to check a particular case for correctness. Sure, this is true. However "moving type checking code into the test suite" means nothing—that would just be type checking.

When you make a code change, there's a difference in the kinds of feedback you get from your tests and your types. Tests usually cover business logic or stories—things that you want or don't want. Types ideally cover everything. They check every operation applied to a given piece of data. Of course types are rarely precise enough that they can catch every logic bug (e.g. strings with semantics not encoded in types, like email addresses).

This is just scratching the surface. You might just have to try out both to get a better sense of how they feel to work with.