Why Chemistry of ENiCrFe-3 as per SFA 5.11 of IIC and ENiCr-3 as per SFA 5.14 is kept different. Major difference between Fe, Ni and Cr is observed in undiluted weld metal also.
One good reason is something you already alluded to. Chemistry. so with an Fe comes reasons to have it such as Inconel or Hastelloy and materials that don't need Fe. but still need the nickel Chrome. Its chemistry, chemistry...