In addition to what Art said: any spaceship that could travel faster than light is also a time machine, and that's a no-no.

Alastair Reynolds is a good example of a science fiction author who pushes against the limits of known physics mercilessly but does not cross them. His book House of Suns has a character explaining at length why there can be no faster than light travel: I suspect that Mr. Reynolds got tired of fan mail asking why he didn't just use spaceships with warp drives...