Besides the initial formulation, this is actually an excellent question.
Purpose: At its core, a degree is to obtain accreditation. So, one can still learn philosophy, or any field at that, without obtaining a degree. It also aids in showing how one can do their homework/busywork, and how they performed in various classes that make up a degree (as well as, perhaps, learning other skills necessary to do well in the real world such as communicating well and working with others). The necessity now, however, is that obtaining a degree in philosophy also includes logic whereby learning from a teacher, doing problem sets, and taking tests is necessary. I will also add that many people who obtain a degree in philosophy use it as a supplement or spring board for other degrees or careers such as economics, mathematics, physics, or perhaps even psychology and sociology.
History: Historically, such as in Greece, philosophy was (and still is) accessible to all such that one simply had to think hard to discover ideas of philosophy. At the time however, one would formally present and write down ideas of philosophy to ensure successive generations could use and build upon the knowledge. Else wise, teaching and learning at that time was largely verbal.
Seated vs Verbal Testing: This question can be applied to other testing of knowledge as well, such as standardized tests. The issue is simply that paper tests of knowledge are more efficient and effective for a variety of reasons. People can read (and re-read) problems and answers or explain their answers through paper better than verbally. So much so that a verbal test would be a disadvantage due to people performing far worse when speaking, or just in front of others. Furthermore, a paper test would likely be faster and thereby can test more things than just a verbal cross-examination. Also, paper testing allows for more people to be tested at one time under the purview of less people whereas a verbal test requires a minimum of 1 on 1 time. As mentioned earlier, testing logic would best, if not needs to, be done on paper. I would also argue that verbal testing would not encompass typical philosophy careers whereby communication or creation of ideas is conducted through written means (see Bloom's Taxonomy).
An Analogy to PHDs: To obtain a phd in a subject, through most means, one must verbally present and defend, through cross examination, their thesis. In this context, it makes sense because becoming an effective researcher or academic contributor means you must be able to communicate your ideas to other people, and perhaps even think on the spot. This prepares one for likely careers or actions after obtaining the degree such as doing lectures or working with others.
Alternatives: At the moment, you can opt to take tests that demonstrate your knowledge for a subject at a college level without actually obtaining a degree. In the US, for example, GRE subjects tests can be taken and are recognized by many employers and educational institutions. I am unaware of such a test for philosophy or sociology, but there seems to be one for psychology in the link I provided.
[Note: I feel my answer is not the best in regards to talking about the history of philosophy in regards to verbally defending or teaching ideas of philosophy, such as perhaps in Ancient Greece. If anyone can expand on that, I encourage them to do so because that is beyond me at the moment]