My thoughts are that we should stop referring to King George lll as the mad king and re-title the film and play. It's a known fact that he suffered from schizophrenia which, in the 1700s, was not a diagnosis.
In any case madness, or rather, the word 'mad' is commonly used to describe a condition where the brain does not function in the usual manner as far a rationality goes, and irrationality is madness.
To object to a word in common use in favour of one which sounds more acceptable (but has the same meaning) is, to my mind, mad.
Like saying 'passed' instead of 'died'. One cloaking the reality, the other laying bare the bones. This is simply my view.