Current and "amount of substance" are base units
The SI system treats both electric current and "amount of substance" as a quantity that is measured in "fundamental" or "base" units. These are amperes and moles, respectively.
Charge has been quantized for more than a century
However, since Millikan's oil drop experiment in 1909, physicists have known that charge is quantized. Perhaps this is still debatable in some forms of exotic string theory or something, but charge quantization is indisputably a reasonable approximation (at least!) for all situations for everyday mundane planetary conditions.
A missed simplification
The SI system already has the unit "mol" to measure "amount of substance". Why doesn't SI treat "fundmental charges" as a substance that is to be measured in moles? That is, why hasn't anyone tried to advocate that the SI base unit for current should be e.g. moles of charge per second?
Moving in this direction would seem to simplify things considerably. We wouldn't need volts; it's just Joules per mole of charge. And so on…
Conversely, if you don't like the unit "mol", you could argue that since charge is quantized, we don't need moles anymore and and can measure the "amount of substance" in Coulombs. A similar simplification would ensue.
So why haven't relevant standards organizations or committees for the SI system considered these types of simplification?
Best Answer
What you suggest is not really a simplification. Perhaps you confuse the SI base units and the SI derived units. The SI base units are a set of seven units from which all SI derived units can be derived (hence their name). The base units are defined by relating them to measurements of fundamental constants. The unit of Volt that you mention, is a derived unit which can be expressed in base units as kg m$^2$ A$^{-1}$ s$^{-3}$.
In addition, if you look at the SI base units and how they relate to the fundamental constants, you see that linking the mole to the Ampère, does not really simplify things. One still need a link to the electric charge of the electron and the hyperfine splitting of Cs.