Alas, I think your intuition lets you down in this instance.
Could be, wouldn't be the first time.
Wormholes are recognised solutions to einstein's field equations...
Right. They are exceedingly theoretical and their plausibility is entirely dependent on our understanding of the theoretical physics involved. I'm slightly skeptical about theoretical physics. It seems to work well enough now, experimentally and observationally, but I'm not sure how likely that is to continue indefinitely into the future. Put a different way, I'm happy to give relativity theory provisional acceptance for the time being, but I'm less comfortable giving any of the pronouncements of theoretical physics absolute acceptance. I don't perceive the heiroglyphs of theoretical physics as eternal and necessary truths, the Word of God.
The problem that I have with wormholes is more practical, I guess. I don't see how a traveler could steer them so as to end up where desired. And opening one would probably require such violent physical conditions that it wouldn't be anything like a
Stargate. (More like a black hole.) You wouldn't want to be standing near one.
FTL travel, though, does not seem to be, at least not at a local level.
The first paragraph in the reply above applies here too. It's true that there are seemingly impossible mathematical consequences to violating the speed of light in Einstein's scheme. But Einstein's scheme seems to me to just be a working out of the consequences of the speed of light being the same in all frames. When Einstein assumed that, he had to do all kinds of counter-intuitive things to space-time metrics so that everything remained consistent. My point is that Einstein's theories are the logical result of the assumptions that he made. It's true that predictions made on that basis have been verified many times, but there isn't any metaphysical necessity that this model has to be an absolutely correct depiction of reality, any more than Newton's mechanics was. That was exceedingly well verified too.
(Wherever he is, Paddoboy is probably seething right now. Maybe I'll lure him back to flame me. Come back, Paddoboy!)
For the purposes of science fiction, I can imagine that the seeming cosmic speed limit might not be inviolate. I don't think that achieving superluminal velocities necessarily implies physical conditions that would kill everyone nearby. And a spaceship traveling at "warp velocity" could still be steered to a desired destination.
Regarding the hypothetical science fiction quantum drive, one problem I see is that while a particle might theoretically be anywhere in the universe, it would presumably have an exceedingly low probability of being most of those places. So if we reduce a starship to a wave function spread out over the entire universe, causing it to manifest itself in another star system would mean causing it to assume a low probability state. For the purposes of science fiction, I can imagine that requiring energy (like raising a mass to a higher potential energy position), so that longer jumps would require more powerful engines or something.
(More power Scotty! I'm giving you all she's got, Captain!)