IUPAC Recommendations for Concentration Units (ppb, ppm)
There are not this kind of problems with the IUPAC recommendation. The only point in it is to specify the parts of  what we refer to, nothing more.
In such a sense it seems clearer than expression as molality or molarity.

Take an amount of atmosphere at given conditions. The concentration of Ar or whatever component can surely be expressed in terms of mole number in a million or whatever number of moles that amount contains.

As for the rock analysis case in the question, note that IUPAC umol/mol is an example, it doesn't mean it should be preferred to mg/kg (or ul/l etc.). The measured amount remains the most convenient both practically and mathematically.

I add that following recommendations would - perhaps - also help clear another practical con of unspecified ppm and percentage concentration values.  Often people forget that 1 l --> 1 kg of solution is acceptable only with very dilute solutions and when the solvent is water and go around telling and even publishing % concentration in various solvent so that the reader must assume a wrong procedure in order to follow up. Explicitly saying mg/kg instead of ppm should evidence that when mg starts to be hundred, than one has to switch concentration units or being more careful when reporting.