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.

The mole was promoted to the status of "unit" in 1971

The 14th Conférence Générale des Poids et Mesures (CGPM),

considering the advice of the International Union of Pure and Applied Physics, of the International Union of Pure and Applied Chemistry, and of the International Organization for Standardization, concerning the need to define a unit of amount of substance,

decides

1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol".
2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.
3. The mole is a base unit of the Système International d'Unités.

It had been in use before that for quite some time, and I guess nobody wanted to change the symbol. Think about the ensuing confusion if you made up a new unit symbol today, that means exactly the same thing as the old one.