The noun "wish" leading subjunctive mood

The following year, 430 BCE, plague came to Athens, made worse by the overcrowding that had come with people entering the city from the countryside. The plague killed Pericles, and passion influenced the Athenians' choice of a new leader, a man named Cleon, a merchant tanner by trade who was more excitable than had been Pericles. Cleon's desire for vengeance and punishing the enemy matched theirs.
One who did not go along with the public's passion was the playwright Aristophanes. Following a playwright's responsibility to be above common opinion, he depicted Cleon as a demagogue and a rogue. And with his dislike of democracy he expressed his wish that leaders of Athens be chosen by less excitable and more moderate-minded men rather than the public.
[The War and a Question of Genocide http://www.fsmitha.com/h1/hell08.htm]

I know the verb "wish" leads conditional 2 or 3.
And the following verbs/ nouns leads subjunctive mood? as, command, demand, insist, request and so.
But I didn't know the noun "wish" led subjective mood.
So, I'd like to know why the noun usage of "wish" is quite different from the verb usage of it.
Thank you in advance for your help.