In The Scarlet Letter, what was the purpose of Hester Prynne's punishment?

While deterrence is an obvious motive for the punishment meted out to Hester, there are subtler reasons behind it as well. These present themselves when we consider the nature of the penalty. After all, there would have been little outcry if instead of pinning the Scarlet Letter on Hester, the town fathers had chosen instead to summarily hang her. One may fairly ask why they choose not to execute her.  First, Governor Bellingham and his associates still hope that Hester will eventually give up the name of her guilty lover. Subjecting her to such an extended term of ignominy will, they reason, increase the chances of Hester succumbing to what they mistakenly believe to her major weakness, namely, her womanhood. Second, there is the question of Pearl, through whose existence they hope to objectify the unnaturalness of Hester's adulterous union. Again, another irony emerges: while Pearl does cause Hester much grief, she also serves as an enormous source of strength and purpose in her life. Finally, Hester's continuing disgrace provides a convenient salve for the collective conscience of a community whose own hypocrisies might otherwise show up more fully without the blazing hotness of Hester's sin on display for all to see.