A diving coach is, in reality, a teacher. The job of a teacher is to help, encourage and assist your students to learn the subject matter that you are presenting. In this case, your subject matter is the sport of diving. As a person who teaches diving, you need to find the best way possible to reach the students in your classroom (the pool).
There is, in my humble opinion, no right or wrong way to teach diving (safety excluded) — every diving teacher is different and every diving teacher has his or her own methods to get the lesson across to the students (divers). Experience has shown me that a student is more apt to learn in an environment where the teacher is enthusiastic about the subject matter being presented and I feel strongly that a diving teacher who STANDS during practice has a much better chance of displaying that enthusiasm to his or her students (divers).
A coach who stands can be more animated and can better demonstrate techniques; can walk over to the diver for some one on one discussion; can jump up and down to celebrate the learning of a new dive or to show dismay at a diver who repeats the same mistake again. In essence, a coach who stands can bring some energy to the classroom (pool) and this can really benefit the students (divers).
Think back to your school days and recall how boring it was to be in a class where the teacher just sat at their desk and read notes for you to copy in your notebook. Now recall those classes where the teacher was a bundle of energy and you could not wait to get in there and learn! NOW GET OUT OF YOUR CHAIR AND START COACHING!!