You didn't identify the analogue to "student pilot." When you are a pilot, for the first phase you are a student pilot, then a private pilot, then a commercial pilot, etc. When you are going through primary school, you are an elementary school student, then a middle school student, then a high school student, etc. In that case, if you use the word "student" it is not at all implied you mean elementary school specifically. However, when you use the word "student" in aviation it is implied that you mean "student pilot" because that's the only level where the word "student" is actually used in the name. If you use the word "learner," the reader does not need to stop and ask "wait does this mean a student pilot or a student beyond PPL." The same problem does not exist for primary school. If you use the word "student," the reader does not need to stop and ask "wait does this mean an elementary school student or a student beyond elementary school graduation."
Again, some people think it's not a big enough deal to be worth making changes. However, if you are not seeing the distinction, you are not understanding my point.