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?

In my understanding, the conflict of interest actually goes in the other direction: if the teacher is not the examiner, then the teacher has a conflict of interest because their job depends on the performance of the students on the exam.

In the United States, tying lower levels of education to test scores has created quite a bit of "teaching to the test," as well as other ethically problematic practices like schools cherrypicking good students and attempting to expel special-needs students because the funding of schools and the careers of individual teachers are both closely tied to how their students perform with external examiners.

As such, I think that it is a very good thing that at the university level and postgraduate level, most education is allowed to be much more customized. Note, however, that in professions where there are strong ethical and safety issues involved, such as law and medicine, there are still external testers but these tests are more holistic certifications rather than individual class evaluations.

In most of my student life I have been graded by my teachers, and in most of my lecturer life I've graded the students I teach to, and I never heard complains of my students nor my fellow students that exams were too easy. In fact, I can remember the opposite: students claiming that exams were too hard. Therefore, I don't see any generalised conflict of interests that teachers grading their own students unfairly raise grades.