Interestingly, a "conservation of matter" law can exist independently of atoms. I.e. it is mathematically consistent to create a universe in which a "mole" is necessary, but matter is not discrete. Therefore "mole" can be considered a bit more fundamental (in any universe). I find it reasonable to stick to using a "mole" unit on that basis, although I would not be dying on this hill.

The yoctomole is a wonderful unit, for example when you want just slightly more than half a cup of coffee!

But the mole as a "counting unit" is different from OP's idea of assigning units to things like network requests. The mole is just a shorthand for a number, like a dozen or a score. We don't have different kind of "moles" for, say, carbon atoms and water molecules. Or coffee.