I was hoping somebody would say that. That is exactly my point.
With Godwin's Law the standard argument is that hyperbole somehow diminishes the plight of those that suffered, but that argument really does not encompass the full breadth of the War On Hyperbole.
Here, for example, I've made an exaggeration with a comparison to sterilizing pets. Is the concern that I am diminishing the plight of pets and their reproductive lives? No, I don't think so, that would be silly. Rather, the objection is to the rhetorical device itself, not merely to the tasteless application of it.