Hmm, similar to how heavier than air flight was thought to be impossible for humans?

Interesting how the will of a few can shape humanity. I love it.

Probably a pretty good analogy! Even now, it's not known whether time has directionality in any way that is meaningful in physics. FTL travel would resolve the "Arrow of Time" question (https://en.wikipedia.org/wiki/Arrow_of_time) but this wouldn't invalidate much/any of physics because the arrow is essentially non-observable at the micro level

Can you give me a reference?

Here, Krauss argues in favor of Lorenz invariance when presented with the possibility if FTL.

https://www.scientificamerican.com/article/ftl-neutrinos/

He discusses it extensively in The Physics of Star Trek.

Also, supposed locally FTL travel for subatomic particles is pretty different from locally non-FTL but globally FTL travel a la Star Trek, Alcubierre drives, etc

>> Causality isn't nearly as central to physics as it may be to your worldview

No, but locality seems to be a sacred cow in physics. They'll latch on to just about anything to explain violation of the Bell inequalities, but nobody is willing to part with locality.

Generally I'm suspicious whenever anyone seems to imply that an entire field is barking up the wrong tree