I think all the policies for SEP a/c I've ever seen have a clause covering an instructor
And I have seen quite a few which only insure the owner(s).
You are quite right that it is very easy to add an Instructor to a policy; but that does not help an aircraft owner who turns up expecting an hour's flight, as PIC, with (someone who just happens to be) an Instructor rather than a dual, training flight whereby the Instructor, not the owner, must be PIC.