An initializer or static method requirement doesn’t technically preclude a protocol type from self-conforming as long as there’s at least one conforming type: the protocol could just pick that type and construct it / call the method on it. But if that type isn’t unique (which is reasonable to assume a priori), picking one type in specific would be an arbitrary choice, so as a policy matter it doesn’t make sense to allow it. So sure, maybe with an annotation it could be done if there’s really a reasonable default that wouldn’t cause more confusion than it saved.
Don’t think about it in terms of a function that takes an actual value of the protocol type. Think of a generic function over T: P. What actually happens if you use a particular requirement when T is dynamically the protocol type P itself?