Why is the the rate of a reaction measured in concentration?
Simply, because if you used an absolute amount (moles, for instance), by changing the quantity of reagents used, you couldn't use the existing data (or you would still need the volumes, to calculate the concentrations, in order to scale up/down the existing data, and fit them with your reaction).

Since the kinetics doesn't change with volumes, but with concentrations (for instance, if you use the same concentrations of reagents in 100 ml, or in 1 liter, the reaction, at least in theory, doesn't change) it's much easier and useful to express it in terms of concentrations.