`According to NIST special publication 330, the choice, ``to a certain extent arbitrary, because it is not essential to the physics of the subject.`` and,``by convention are regarded as dimensionally independent.`` Which is to say that they just are  and you are not to ask questions. You are poking here at the rather tender underbelly of the SI. The units are not, as you point out, in fact ``dimensionally independent,`` however, we wish they were and keep them seperate to allow for accruate measurements, and convention. Another sore topic is temperature. Why are there two systems? What sense does that make? It's just like the tradiational system of fahrenheit, except that the afine transformation is simpler and people liked it, so they held on to it b/c it wasn't that bad.   `