FTL is equivalent to time travel into the past. If you have one you have the other.
People thought humans wouldn't break the sound barrier for engineering reasons, not because the laws of physics prevented it. And just because people in the past thought something was impossible doesn't mean it will one day be possible. 100 years ago, physicists thought perpetual motion machines were impossible.
Thanks for saying what I wanted to. Everybody who knows nothing about physics always brings up the "humans can't possibly travel faster than 25mph" thing when someone who does know talks about violating causality, but as far as I've seen it was only printed in a newspaper or two, not espoused by physicists. The speed of light limitation is a necessary part of one of the most precise and thoroughly tested theories of all time.
People thought humans wouldn't break the sound barrier for engineering reasons, not because the laws of physics prevented it. And just because people in the past thought something was impossible doesn't mean it will one day be possible. 100 years ago, physicists thought perpetual motion machines were impossible.