I don't find arguments against a possible FTL future on the basis of its 'conceptual impossibility' particularly compelling. Of course it's wrong to suggest that it just takes more power or whatever to solve it, it does indeed require a new concept of how the world works. The argument from past impossibilities disappearing is still potent, not on the basis of any formal logical proof, but on that of a robust preponderance of evidence. It happens every time. We define the limits of our world through the lens we happen to experience it through. It was conceptually impossible to sail around the world when we thought it was flat. The solution wasn't more power, it was to revise our understanding of the world to one that was more correct.
I don't know if the same possibilities exist for this problem but there is no reason in principle why they can't. Of course the predictive and explanatory abilities of modern physics reach much further than any before, but even they aren't perfect, are tainted by dogma in the face of conflicting data, as the greater and greater necessity of more and more dark matter to explain discrepancies in the data proves. Such 'discoveries' sound an awful lot like the epicycles of old to me.
The point is that our current understanding of the universe, as broad, deep, and robust as it often seems to be, is not some axiomatic collection of truths read from the language the universe was written in. They are carefully created, endlessly tested and observed, but nonetheless merely constructed by limited and biased human minds. Like so many theories, so many so well known truths before it, our current understanding of the universe is absolutely subject to reaching the end of its usefulness, its ability to accurately explain and predict.
We are such tiny, limited creatures, so limited by our perceptions; what we think we know of the universe today may describe merely the barest beginnings of the totality of the cosmos. With our five little senses, our three little dimensions, we may merely be floating on the surface of an endlessly deep cosmic ocean.
So yeah, impossibility most certainly is a constantly receding bright-line. Sometimes it inches along, and sometimes on the back of one person's one moment of insight, followed by a lifetime of effort, it can be pushed by leaps and bounds in what amounts to a moment.
I'm no scientist of course, and can only defer to those more knowledgeable on the limits of physical causation. Causation, though, isn't just a variable in an ad hoc equation for the universe, it is a concept that doesn't require our particular physical 'laws' to exist. And as a concept, it doesn't have a speed limit, a unit of time doesn't have finite dividability.
Don't mistake me, it might be that everything is as it seems, and this impossibility will never be retired. But nothing, nothing in our physics, however thoroughly considered, nothing in our observations, no matter how often repeated and documented, makes it impossible in principle.