The "problem" with General Relativity is that it is so general it can describe arbitrary universes exactly, but doesn't in itself provide a way to tell if an exact description is a good match to our universe. So we have to use some heuristics to reject candidates.
For example, general curved spacetimes have any number of space and time dimensions. General Relativity will let you exactly solve the geometry of a universe with one dimension of space and one of time, or ten dimensions of space and two of time, and so on. However, we have excellent (and so far never contradicted) evidence that our entire observed universe must be in one of a very particular family of general curved spacetimes, those that are Lorentzian. Lorentzian spacetimes have three dimensions of space and one of time. When we examine a solution to the Einstein Field Equations and see only two dimensions of space, or twenty-five dimensions of space, we can reject it as unphysical.
Next, there are an infinite number of possible Lorentzian solutions to the Einstein Field Equations, and we can make some very silly ones. We can reject any that are spatially smaller than a breadbox, for example, or which have a total existence of about ten seconds, or in which literally nothing ever happens for eternity. Indeed, we can reject a Lorentzian spacetime as unphysical if its properties could never produce galaxies (since we see those, and live in one) and the conditions for creating galaxies includes chemistry, nuclear physics, and so on. There are lots of possible Lorentzian universes that can produce "us", but lots more that cannot, and we can reject those as unphysical (because we exist; this is a flavour of the Anthropic Principle).
Relativists, however, like to work with simplified models to make calculations tractable, even if those simplified Lorentzian universes are obviously unphysical. Most of them are vacuum solutions (i.e., there is zero matter content at all, so therefore no galaxies), or use some very simple splash of matter (the Standard Cosmology models the matter content of our Lorentzian universe as a handful of smooth fluids, ignoring the relatively small-scale lumpiness of stars and planets). These models are manifestly unphysical, but [a] still usefully approximate observed physical systems and [b] typically can be made to more and more closely approximate our physical universe (or at least a region of it) perturbatively, meaning that we can add things to the simple model making it much less simple and a little more in accord with observation and experiment.
But how do we connect a manifestly unphysical model with an apparently physical one? Heuristically, again. Among the things we expect to decide whether a Lorentzian spacetime is physical or not are various energy conditions [1]. When a region of some arbitrary Lorentzian spacetime is determined to violate some energy condition, its physicality is in doubt. It may be possible to rescue such a region of spacetime in some cases, but most of the time one would not bother. "Seemed promising until I found it violated some energy condition at galactic scales (kiloparsecs)" can still be good for developing intuitions or numerical methods or whatnot, and might even work as an effective theory -- reasonably modelling our physical universe -- at a much smaller scale (like in a star system, at the scale of tens of astronomical units or microparsecs) or a much larger scale (like at the scale of tens of billions of light-years or gigaparsecs).
"Warp drive" solutions similar to Alcubierre's are vacuum solutions which are almost always a bump function on an otherwise perfectly flat Lorentzian spacetime. For short trips from near some outer planet of our solar system to near some outer planet of a nearby star system (scale of parsecs), the presence of gravitating matter nearby the path of travel can be treated as small perturbations on this model. So heuristically, we look OK. However, the "warp bubble" in these solutions are eternal features of the spacetime, and that's both a giant warning sign of unphysicality (is any complex structure eternally old in our universe, given that everything we know of is consistent with a hot big bang in the finite past?) and also completely useless for the purposes of on-demand travel. So, we ask the question: how does one go from a vacuum flat spacetime to a spacetime with a suitable bump function?
Here one takes a "sources-first" approach, where sources are matter and anything else that generates nonzeroes in the stress-energy tensor that sits on the right hand side of the Einstein Field Equations. As a slogan one would put this as "matter tells spacetime how to curve". So what type of matter can create a bubble?
As one investigates this question, one generically runs into a violation of the positive energy condition. I would describe the postive energy condition as "the joint ground state of all the spacetime-filling fields serves as a floor, and no local perturbation of this state leads to a globally-lower energy", or "empty space is really really cold, and adding things to it can only make it hotter rather than colder". A solution which upsets this -- negative energy -- is something never seen in any experiment since the discovery of the second law of thermodynamics, and negative energy is so torturously hard to sweep under carpets like non-isolation or vacuum energy that after a while it must begin to feel self-deceitful to keep pursuing a region of spacetime that contains it as anything other than an unphysical model.
Apparently people who try also run into comparable problems when trying to (for want of a better word) steer a warp bubble that exists (ignoring how to make it exist in the first place, or how to make it cease existing at some later time). I'd wager the model runs into trouble for trips between galaxy clusters, by virtue of interacting with the metric expansion of space: having to make big changes to simple models to accommodate the cosmological constant is a common pattern in the history of General Relativity.
There is something of a literature on problems like this, and while it's interesting in the sense of hunting for heuristics to shoot down other seemingly physical solutions to the Einstein Field Equations, I don't think it's very interesting to keep looking for loopholes to try to save the family of Alcubierre-like spacetimes. Beating a dead horse into some sleek-looking and seemingly aerodynamic shape won't make a stagecoach be more likely to reach Mach 6.
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[1] https://en.wikipedia.org/wiki/Energy_condition#Motivation