Why are enthalpies of reaction or Gibbs FE change given in kJ/mol
It makes perfect sense that the units KJ/mol are used.

If you burn 2 cords of wood you get twice the heat as from 1 cord of wood.  

Enthaply (and Gibbs free energy) of the reaction is proportional to the number of moles that react.  

If the reaction is written as:

3A + 2B => 6C

Then the change per mole would mean: per 3 moles of A = per 2 moles of B = per 6 moles of C.