Doctor and doctrine have the same root: to teach. In Latin "doctor" meant a teacher. So the origin of the term is from gaining a degree relating to teaching. As for why we use Ph.D. and not specifics, well... in some countries "Doctor of Science" is used, but when you think about it, when you get to a certain level, most schools of thought become philosophical in nature. We're actually studying the core issues at hand (hopefully) and asking ourselves if and why what we think we know works. That is philosophy.
History: In olden times a person might expect to make significant contributions to a range of different topics. A paper on medicine here, another on astronomy. As the body of knowledge grew, this became less achievable. Everyone is now stuck in their niche. However, we still have the tradition where the terminal degree is the Ph.D.
Philosophy abounds in science. Please write a 1500 word essay on why we should (or should not) declare a significant difference if some fancy number is less than 0.05. Such an essay will be a mix of mathematics and opinion. Several threads on RG have tackled this task if you have some free reading time. There are also the assumptions or opinions that abound within specific disciplines. Simple disagreements like Reaganomics, or Keynsian economics are philosophical. How is this part of the world connected so that it functions in the way that we observe it to function?