One of the problems with this approach that has been explored in other papers is that even if you have a warp drive and even if you have actually gotten a ship into it and even if you've managed to point it in the direction you want to go, the collision of the interstellar medium with your warp field tears it apart quite violently and the warp field "collapses". And unlike when they "collapse" on Star Trek and the only manifestation is a polite electronic "whirring" noise, being in a collapsing real warp field is a death sentence, with tidal forces on par with black hole gravitational fields.

Bear in mind, this article only addresses one of the many fundamental challenges to the Alcubierre drive: the energy requirements. Typically, the energy requirement has been considered the primary challenge to the feasibility of the device. But it's not the only one. Science hasn't completely worked out what would happen inside the bubble, or what happens to particles of matter interacting with the bubble at its leading edge. I've heard at least one speculation that the bubble would fill up with Hawking radiation and pretty much roast everyone alive inside it, like a big, interstellar dutch oven.

Another issue is the stability of the bubble itself. Again, the article doesn't really address this issue. But it's a pretty big one.