Its a comparison to other people who traditionally work on heads, the headhunters and headSHRINKers of South America, who would shrink their captured heads for trophy, ritual or trade purposes. It is a shortened form of headshrinker, which was once a popular moniker for psychiatrists.
My preferred terminology for a trip to the shrink. Is “a check-up from the neck up.”
Goq; obviously if the slang was chosen “because they reduce their patients problems” they would’ve been called “Shrinkers”
Since the title is shrink, I propose that it referring rather to their own intellect which seems to shrink as they practice their profession, requiring them to see other shrinks themselves in the hopes of finding what they seem to have lost over the years.