It's really terrible that these are so clearly broken, and yet they are still used. It's a whole field jerking itself around. It reminds me of the phrase, "Something needs to be done. This is something, therefore this needs to be done."

It's remarkable that pseudoscience is a big part of how we (don't) protect our rights.

To rant for a second, it seems like a case of what I encounter at work too often as a data scientist. It drives me nuts. There's some statistical fallacy where lay people infer one thing, while the logical inference is something else for some subtle reason, and they respond to the critique with, 'well, yeah but we don't need a super rigorous answer here,' or something along those lines. As if a wrong answer is more correct when you 'don't need rigor.'

I think we're in that boat because people so easily mistake approximate correctness in the sense of 'this answer is very nearly the right answer' with approximate correctness in the sense of 'this reasoning is very close to the right reasoning.' The two are interchangeable often enough to create the bad habit, like if you discard an assumption that is very probably true enough, or discard a term that is small. But when they aren't interchangeable, they're really really not interchangeable.

(We're also in that boat because enough people cry wolf about rigor in the other direction, like complaining about discarding an error term that really is small enough to safely/rigorously discard)