Doctors are also important. And nurses. And the admin team. And the cleaners....
But I agree, cleaners should be more respected.
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?
Having a trashy ward - is much more likely a failure of the management / admin team in training & superversion than it is on the cleaner specifically.
Not saying you should treat cleaners poorly, but it does explain the wage level.