Well, if you want to get right down to it, and rely on "current tech," faster than light travel as portrayed is impossible. Period. Even if it were half-possible, the time changes would preclude anything like a meaningful dramatic timeline.
So we might as well not debate dilithium.
Well, not really. There are plenty of theories as to how FTL travel could be achieved, in fact, Star Trek's warp drive was/is based on discussions with scientists as to the most plausable way this might be achieved,
in the future.
Notice I had said "extrapolate" from current tech, not "rely on it". There is a world of difference. Period.
While it is true that it is currently beyond our tech, there have been advances in our understanding of such things that suggest we are on the right track, and that this is definitely the way to go toward that future goal.
Also there's a difference between "warp drive" (both theoretical and fictional) which circumvents the time changes you refer to, and "relativistc drives" which would cause all the problems for dramatic timelines.
As for debating dilithium or not. While it's true that it started out as a plot device, it's evolved into a much more important "element" in the trekverses, so it's worth discussing and debating IMHO.
If there's one thing we should have learned in this thread, it's that there are several scientifically plausible explanations as to how something like this could really work. While I'm sure "dilithium" will never be used in a real (future) FTL starship, it is not beyond the realm of posibility that some sort of crystal regulating or tuning function may be indeed be employed?