The reasons for choosing length, mass, time, temperature, and amount as base quantities look (at least to me) obvious. What I'm puzzling about is why current (as opposed to resistance, electromotive force, etc.) and luminous intensity (as opposed to illuminance, emittance, etc.) were chosen to be base quantities. Does it have something to do with them being the easiest to measure?
Answer
Historical issues I suppose; indeed current definition of ampere is rather stupid (force between two cables in vacuum) in light of the fact it could be done with number of elementary charges per second.
Candela is even worse, because it involves properties of average human eye (so called "luminosity function") -- so in principle it changes instantaneously as people get birth, die and their eyes age (not to mention various eye/brain fractures and treatments).
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