Well, it has been more than 40 years since I read the book, and some recollections remain clearer than others. I have read other works by Hawthorne more recently.
Yes, there is an element of melodrama, all right. Popular writers of the time (his contemporary Dickens, for instance) did go in for melodrama and tended to draw their villains much more heavily than is typical today. There were different standards of believability then. People didn’t expect characters to resemble their neighbors and local townsfolk quite so faithfully while also bearing the burden of symbolism and moral teaching. The lessons of sin, estrangement, and redemption are perhaps a bit larger than everyday realism in The Scarlet Letter.
But also remember, what might seem overdone now was not necessarily out of proportion or a cliche when the book was published in 1850. Being one of the most influential American writers, Hawthorne has literally influenced many, and so literature has evolved in the past century and a half. What would be very strange is if we were still writing now the way he did then. You can’t really judge his work as if it had been written last year.