Expression that means something like "killing the sheep to keep them from being kidnapped"
I'm looking for an expression that conveys an excessive risk management approach that ends up having a worse effect than what it is trying to protect against.
Solution 1:
A common saying that comes to mind is The cure is worse than the disease, which thefreedictionary says first appeared in Philip Massinger's 1624 play The Bondman.
Solution 2:
"Cutting your nose off to spite your face"?
Cutting off the nose to spite the face" is an expression used to describe a needlessly self-destructive over-reaction to a problem.
Sounds like a good fit to me!
Solution 3:
I agree with @FumbleFingers for the general case; "the cure is worse than the disease" is well-understood. If you're looking for something a little more colorful (akin to your title), "we had to burn the village in order to save it" is a US expression arising from the Vietnam war. (As noted there, this is not the original formulation, but it's a common version.)
Solution 4:
I'd say you're throwing the baby out with the bathwater, in that you're accomplishing your goal but doing it in such an overly thorough way that you end up with very negative consequences.