Earlier quoted context omitted.
Doctors are harder to train, as such they are a rarer resource, and more expensive. We can freely pay cleaners less, and purchase more doctors. Isn't that how it works?
Yes, but hiring more doctors is counterproductive if their work is regularly being undone because of bad sanitation. In such a case, a dollar invested in cleaners buys a greater fraction of lives than same dollar invested in doctors.
the dollar equation is relative, i.e. "in such a case". The balance point still ends up with doctors being payed more, and cleaners significantly less.
Plus, who guarantees that dollar cleaning improvement? Maybe all you'll be doing is setting a precedent for higher pay - you need more to correlate with better cleaning. Maybe regular (independent) inspections & testing?