Why is a nucleophilic substitution reaction between ammonia and benzene unlikely?

A nucleophilic substitution reaction is when a nucleophile (an electron pair donor) replaces an atom or part of a molecule. In this scenario ammonia (NH₃) is the nucleophile as it contains a lone pair of electrons on the nitrogen atom and it is trying to replace something from benzene. However benzene contains a ring of delocalised electrons that exists either above or below the planar carbon ring. This is a region of high electron density that will repel other electrons. Hence ammonia cannot attack benzene as the lone pair of electrons in an ammonia molecule are repelled away by the ring of delocalised electrons. This makes a reaction between the two heavily unlikely and it also explains why benzene usually undergoes electrohilic substitution reactions as opposed to nucleophilic substitution as only a strong electrophile (electron pair acceptor) is capable of being attracted to the benzene ring.