If there are types that allow you to not care about the type, then why have a type?

The type represents a set of properties about the inhabiting values so if you have an opaque value you don't want others to inspect, wrapping it in such a type makes that explicit throughout the rest of the program. That information is not available if every value in your type has the same type. Presumably though you will actually attempt to do something with the contained value at some point so you must have some expectation about what it is.