It seems that the reason is that chemists don't care how many atoms there are in their reactions. It would be inconvenient: fractions of atoms don't make sense, and the numbers are far from human scale. They just want an agreement, so that even if they don't know the exact number of atoms in their test tube, they know they all have the same number. That's what units are for.
The definition of units are done in the most convenient and precise way possible. And they are updated as science progresses. For the kg, the artifact used to be the best we had, alternative methods weren't precise enough, they changed that to the Kibble balance because now, it is better. It may change again at a later time if we find something better.
Back to the mole, it used to be defined as the ratio between the kilogram and the mass of a 12C atom because it is the best we had. Now that we can count atoms with more precision, we decided to change it to just the Avogadro constant, which becomes fixed. Again it might change. What may happen (or may have happened, see Avogadro project) is that we can define the kilogram using the mole, making it fundamental.