Wormholes and Alcubierre warp drives are both constructs within the framework of the currently-accepted physical theories

Err no they are not. First of all the all violate energy principals widely accepted to hold. Second they need *negative mass* that has *zero* theoretical underpinnings. That is, withing the currently accepted physical theories they are quite impossible. Then add the fact that the basic Alcubierre drive needs more energy than the visible universe and is causally disconnected from the rest of the universe....

We find maths that describes reality, not the other way round. A good example is how high will a ball go when thrown upwards at a given speed. One of the solutions can give a complex number. We just ignore it as physically impossible.

Just because the math has a solution in some abstract mathematical sense does not mean is represents anything to do with reality.