What is at stake is "Some scientists should consider FTL travel possible, and give it a go." for such a statement, the argument definitely holds water.
If something was FTL, and we need light to see things, how could anything FTL be seen, as light could not move fast enough to reach it then reach our eyes. Further, assuming we could travel FTL, while traveling we'd be nearly blind, and anything we did see wouldn't make any sense.
Basically you'd see the same thing from multiple locations, as the light emitted closest to you will hit you at the same time light emitted in the past from further away reaches you. It would construct as two objects going in opposite directions.
Just because something is moving faster than the speed of light doesn't mean the light reflected from it never reaches our eyes.
I think another way to perceive it is as if you have a buffer that is beginning to overflow because you can't empty it faster than the speed of light. That overflow is how I'd imagine you'd detect FTL objects. It's like the visual equivalent of a sonic boom. Again idk what I'm talking about, but it was nice to think about :)
We have observed at least one FTL phenomenon -- sort of. We know entangled particles communicate with each other FTL because of the Bell inequality. We just don't have any influence on what message they communicate (and we probably never will).
This could be the case in reality. But its utterly useless information, because it doesn't really give you a direction in which you can even begin to investigate it. Saying that something is possible in this regard is saying that our knowledge of our reality has holes, and "anything" can be in those holes, nothing about the specifics of what could be in those holes.
Personally my biggest question would be why didn't we observe anything FTL in the Universe yet. But it could be, just like with many scientific discoveries, what has been a great data point has been dismissed as some measurement problem.