Even observation isn't completely error-free, which is another reason why it's not the "source of knowledge" that empiricists would think it is. Your senses can fool you, although that problem is far less than the Ancient Greeks thought, and then there are completely mundane things the government is keeping from you - like them researching new weapons that look futuristic but are still from Earth. If someone (even a military pilot) saw something like https://en.wikipedia.org/wiki/Northrop_YB-35 in the late 1940s, they might have thought that this couldn't possibly have been developed by humans.A lot of pilots, and I mean a LOT of pilots have witnessed things being done by objects in our atmosphere that are far more advanced than anything our own tech can accomplish, and only perhaps a handful of real shot callers in any given government would be allowed to 'know' the truth, some of whom might be held tightly to keeping that secrecy against their will by extremely strong tactics by the few that do know the truth. There are lots of public whistleblowers as it is, but they are summarily ignored as attention grabbers.
We always knew that 70 mph could be reached in nature, e.g. by a cheetah. This speech can be reached by exerting a certain amount of force over some time, taking into account your mass, wind resistance, the friction properties of the ground etc. There is no problem with causality, and the established theories have no problems with that. The same was true 200 years ago when the established theory was Newtonian Mechanics. The fact that some ... people who were clearly non-scientists made some apocalyptic predictions about faster speeds (especially when not reached by using a horse) does nothing to change that. We have a better understanding of nature today but these people clearly have their successors in today's world. Does that devalue our current theories?100 years ago, traveling at 70 mph across land being accessible by a common citizen would've been thought to be a total fantasy that would NEVER happen. Our entire history shows us we continue to advance on every front as we go and should not deign to think there are any such thing as unbreachable limitations.
We don't just have the vague idea that FTL travelling is impossible, we have an established understanding of the world (leading to many testable conclusions that were successfully tested - or perhaps unsuccessfully tried to refute) that is based on faster travelling speeds making no sense. And not just travelling of persons, but of any kind of information. These theories are of course to be considered temporary, but the observations that were made based on them are not. Any further theory would have to be in accordance with them.
There might be a way "around" this with the Alcubierre Drive (which is not, as the name suggests, an engineered solution, but "merely" a solution of the laws of the General Theory of Relativity), but this is more about using a shortcut than accelerating beyond the speed of light. This is highly speculative, needs a lot (about one Jupiter mass per ship) of unconventional matter which we are not sure if it exists at all, and might still be doomed because of massive radiation problems.
We have been exposed to radio waves for more than a century, which is still longer than a human lifetime. If health problems are not established by then, what (potential) health problems are we talking about?I know we don't currently believe there's a health problem with radio waves now but who knows in 50 yrs what we might think.