The physics behind the Alcubierre is all theoretical, and when you're dealing with Theoretical Physics of any kind, there are assumptions in the mix until you have provable theories.

Think of it like a logic chain: "If Z is possible, then Y is possible, and so is X, but that's all supposing we can make W happen first..."

So you can have different pieces of the puzzle provable by math alone, but not all the pieces will together without real world experimentation perhaps. Like how know that Fusion power is possible (we can observe it mathematically and in the Sun), but we basically have to take a bunch of blind leaps to actually make it happen.