The mole was only recently promoted  to the status of "unit", together with the redefinition of the kg etc. 

Before the mole was just an abbreviation for "amount of substance containing Avogadros number of the particles in question", and "mol" was always used in the same way as a formal SI unit symbol, without actually being one.

I guess that's why nobody invented a short symbol for it in the old days, and now it's too late. Think about the ensuing confusion if you made up a new unit symbol today, that means exactly the same thing as the old one.