Why are (university-) teachers also examiners at the same time?
At least at the university level, I think the biggest issue is practicality: who is going to write and grade the exams, if not the professor in charge of the course?

I think this is especially true in things like humanities courses, where the content is so often individualized according to the professor's interests and preferences. (The same thing also happens in STEM courses, but there's often much less freedom in what can be covered, often for "continuity" within a larger degree program.) 

For example, say I'm teaching a French literature course with a specific set of goals (at least in my mind). How much information do I have to communicate to someone else, so that this other individual can write an exam that fairly assesses what the students have actually studied, as opposed to what the examiner thinks they should have studied?