The motivation for any writer is always an elusive point. Hawthorne, a reclusive man who spent some key years (1834-1845) in doings not fully revealed, is harder to pin down than most. "The Customs House" suggests some motivations, however. The narrator, a customs inspector like Hawthorne, expresses some embarrassment and guilt about his ancestors, whose name was Hathorne--N. H. added the "w" perhaps to separate himself from them--having supported the burning of witches in the 1600's. Moreover, "The Customs House" suggests an identification between the superfluous art of writing and Hester's gratuitous and sinful embroidery of the A. The narrator puts the A on his breast, like Hester. The writing is both an exorcism of the sin and the reenactment of it.
It must be said that "The Customs House" is part fact and part fiction. Defensively, perhaps Hawthorne makes it harder to determine just what motives he had, just as one cannot always figure the motives in _The Scarlet Letter_ and some of his other tales.
