We have to remember that not many children attended school or only attended school until the age of eleven and even before hat age they would be out in the fields helping with the harvest of, etc.
Another thing to remember is that church vicars, padres, preachers, etc., moved away from the birth places to give guidance in other parishes and did not know the then very strong local dialects. When I was younger, when Television reception had not reached every place in Britain, I went to a village only two miles from the place I lived in and couldn't understand a word they were saying !!!!
Additionally when I was growing up practically every word, given name and surname, was given the local colloquial "ee" on the end doggie, Charles/Charlie, surname Cram = Crammie., etc. The younger generation might have been fed up of having to correct other people's pronunciation of their surname that they agreed to change it to accommodate the locals.
The origin (below) states it could have been a Norman word and the Normans were French - many French verbs and other names end in the sound "ee" , e.g. "ez", "et"
It will be interesting to see what other chatters think.
SURNAME: Brockett
English (of Norman origin): from Middle English bro(c)ket, a term denoting a stag in its second year with its first horns (diminutive of Old French brock), probably applied as a nickname.
