smitten with/by

It is not a choice, it is usage. According to Google Books, especially from the ‘80s.

This site suggests the following nuances between “smitten with” vs “smitten by:”

Both smitten by and smitten with appear to be acceptable. Smitten with may be slightly more common, but not by much. If you feel the need to make a distinction, being smitten by someone could imply some sort of action on the part of the adored person; being smitten with someone could imply that he or she is unaware of your affection and has done nothing to encourage it—but those aren't hard-and-fast rules.

(quickanddirtytips.com)