I am skeptical of this claim because in the 1700s the urban population would have been minimal compared to what it is today. A large majority of people were employed on farms.
It’s wild how different the numbers were.
NYC's postal names are a mess: Manhattanites can write "Manhattan" or "New York". Brooklynites are supposed to write "Brooklyn." Queens denizens write the historic names of the farm towns that used to be there. "Astoria" is actually part of New York City, even though seeing a letter addressed there might make you think it's a town upstate.
The postal service is older than the current boundaries of New York, and they never updated the mail routing to reflect the unified city.
Before the bridges were built, much of what's now NYC was very rural.