Designing a functional FTL drive with the knowledge of today is the equivalent of a prehistorical human observing a lightning strike and then speculating about electrical household appliances. Yes, we have made some observations, we can even grasp some of the phenomena intuitively and mathematically, we do have some idea of the power behind the thing, but actually accessing it and doing things with it is so far off it's not even funny from today's perspective.
So yeah, if you told a cave dweller that some day everything on earth will be powered by vast amounts of electricity, he'd have to assume this would involve incinerating the planet too.
There is no parade to rain in on, but I do think it's premature to argue categorical impossibilities like the one you're citing - not only from a logical perspective but also historically people like you have almost always been proven wrong. People like me also get proven wrong all the time, the only difference is that sooner or later something almost like the thing we envisioned does come along. Let me put it this way: tech/sci optimists are always on the advance, whereas naysayers have to retreat constantly.
The Alcubierre drive is just one approach to warp drives that we cobbled together with our extremely limited understanding today. If we knew a lot more about the nature of gravity and spacetime (and let's face it: to manipulate it in this fashion we'd have to) I'm sure we'll come up with tons of new ideas.