If nothing else, humans have a penchant for finding windows when the universe closes doors. There is so much we have yet to discover about our universe - one of those discoveries could potentially lead to another form of FTL in case the warp drive doesn't pan out.
I agree, which is why I find Alcubierres proposal interesting. If "effectively" travelling FTL (because you never actually truly do) is possible, then it would have to be possible within the existing understood rules of physics. You can't just violate a theory as obviously correct as general relativity. So, the sensible place to start looking for a way to do it is by solving the equations for loopholes of sorts. Which he did, and which Einstein himself did with the wormhole.
So, within existing theoretical frameworks exist two independent solutions that do not violate physics. I have no doubt that further solutions exist or further insight could be gleaned as we understand more about the universe, perhaps when we have a correct quantum gravity theory. Interestingly enough, both traversible wormholes and the Alcubierre drive necessitate the existence of "exotic" matter, which we never would have thought of without having an open mind to such things - whether or not it exists is irrelevant.
So, I 100% agree. Closing one's mind is the most assured way to never developing technology that would allow us to effectively travel FTL.