There are cases in which you can relate dimensionless units. For instance, moles is a dimensionless unit, it just means times 6.022*10^23. But you can relate moles to moles in some cases, for instance with electrolysis. If you know how many electrons are being pumped into a reaction and you want to know how much Fe(II) becomes Fe, then you can compare moles of electrons to moles of Iron, even though neither moles, elements, or electrons can be related directly to one another in the conventional sense of m/s. In the same way one can relate dollars of one thing to dollars of another and get a meaningful answer.
You are right to point this out though, it is skirting very close to the gray areas of dimensional analysis without being explicitly mentioned as doing so.
There are cases in which you can relate dimensionless units. For instance, moles is a dimensionless unit, it just means times 6.022*10^23. But you can relate moles to moles in some cases, for instance with electrolysis. If you know how many electrons are being pumped into a reaction and you want to know how much Fe(II) becomes Fe, then you can compare moles of electrons to moles of Iron, even though neither moles, elements, or electrons can be related directly to one another in the conventional sense of m/s. In the same way one can relate dollars of one thing to dollars of another and get a meaningful answer.
You are right to point this out though, it is skirting very close to the gray areas of dimensional analysis without being explicitly mentioned as doing so.