> seems like a high level of collateral damage
I do recommend you pick up the book and give it a read (it's great), as Horowitz does go into a lot of detail on when the "shocking rule" strategy is appropriate and the considerations. I won't do as good a job summarizing here but I'll try.
It's true that this inflicts collateral damage. That's part of the point. The fact that you're willing to inflict collateral damage to preserve/enshrine a norm is shocking, and that demonstrates the commitment to that norm.
You definitely should not play this card often (ideally never, but you should have it in your playbook).
The action is shocking, and you'd expect many employees to be shocked. They will discuss the event because it's shocking, and so your decision will be well-known and the news will be self-perpetuating. (And maybe some will leave who don't think that it's a big deal to call women "bitches"; this is a good thing, you have made your cultural norms clearer, and employees who realize they are not a cultural fit will tend to self-select out at the margin.)
Note you can use the "shocking rule" principle in non-ism enforcement too, e.g. "mishandled customer PII => instant fired", "plane crashed due to failures in the QA process that was your core responsibility => instant fired" or even Bezos's famous "All Amazon internal services will communcate over public APIs, if you don't do this you're fired". Not making any specific claims about whether these are good reasons, but just pointing out that whatever norm you want to enforce that are critical to the company's/org's survival, you can use this principle to fuel a dramatic culture shift. You don't get to play this card often though, so be sure that the shift is worth it.