Why do people who find it hard to hear say they are "hard of hearing"?
Solution 1:
It's a common construction from Middle English that is used not-so-unextensively as you'd think:
Fleet of foot.
Yorkshire born and Yorkshire bred, Strong of arm and thick of head.
Etc.
Solution 2:
Interesting question. Etymonline's entry on hard explains that the phrase hard of hearing "preserves obsolete M.E. sense of having difficulty in doing something." This doesn't explain why it is only used for partial deafness. Maybe its alliteration lent it such long life.