Why do we care about black hole interiors' physics? Whatever happens in there is not falsifiable nor provable to the outside. If for (amusing) example the interior consisted of 10^100 Beatles clones playing "Number Nine" backwards, do we know how to unscramble the Hawking radiation to divine this? The same question applies to this new firewall furor. So of what use is a description of the interior to our physics on the outside?
The only possibility of usefulness I can see is if our own universe can be described as an interior up to the cosmic horizon in de Sitter space. But that's only an "if".
 A: Whatever happens in there is not falsifiable nor provable to the outside.
General relativity predicts this, but a) no one has ever checked experimentally, and b) it seems to be incompatible with the rules of quantum physics.  Every attempt at mixing quantum theory and GR has produced results like Hawking radiation that tell us that the black hole interior and exterior are not completely decoupled.
A: Simply because our final goal is a set of laws of physics that describes any part of the universe equally well. Let's say a physicist jumped into a black hole and saw that the interior of the black hole was composed entirely of John Lennon clones. His last thoughts before getting spaghettified would be "why?". From his perspective, physics is incomplete.
Sure, we probably can't use it to predict anything -- but modern physics is much less about predictions and much more about having a beautiful, mathematically rigorous model of the universe. Mathematical models with discontinuities usually aren't "beautiful", and John Lennon in black holes counts as a discontinuity if we take general relativity as our mathematical model of the universe. Which would mean that we will eventually have to replace our model (which is why knowing as much as we can about the inside is important). Besides, if our current theories partially fail inside a black hole, we need to patch that up.
A: Why do we care about the physics inside black holes?
By Karl Popper's reckoning and the rules of general relativity, we probably shouldn't. From the outside, it's not being scientific to theorize about the inside. Whatever happens there is not falsifiable; not just difficult to falsify (like physics at the Planck scale or theories about the inside of the sun), but impossible in principle.
It may be mathematically useful for other reasons or philosophically interesting but it's not, according to Popper, scientific. If suicidal people jump in and survive, fine, it's valid science for them (while they last) but for us on the outside, it will never be scientific to theorize about the region.
That should be sufficient reason not to care, but there's something even more fundamental. Beyond the falsifiability issue, the greater reason not to care about the inside of a black hole is the more and more likely scenario that there isn't any inside to care about.
Raphael Bousso muses that space and time seem to "somehow" end at the horizon. And Joesph Polchinski sums it up this way: "... the inside of a black hole — it may not be there" ... "Probably that's the end of space itself; there's no inside at all." 
Granted, these new ideas are speculative and controversial but what, really, is the evidence that the spacetime manifold does continue across the horizon? That looks to me like an unexamined assumption. The idea that an in-falling observer simply drifts on through the horizon assumes continuity of the manifold. The same assumption is there for the theory that entanglement bridges the horizon.
GR tells us that in-falling matter and energy never reach the horizon; firewall theory puts a vaporizing surface there; the membrane paradigm and stretched horizon theories completely ignore the inside and describe a one-sided surface with physical attributes; and Lynden-Bell and Katz's calculations put the mass of a black hole entirely in its external gravitational field.
These ideas strongly hint that there is no interior to worry about.
Unfortunately, all of this will upset a lot of very smart people who have invested so much time in theories about the interior, and rightfully so. But it also presents a great opportunity. If black holes are actual holes or cavities in the spacetime manifold, it ushers in an entirely new and untapped paradigm to explore. We live in interesting times, indeed.
A: There used to be a branch of mathematics called "Surgery on Manifolds". Well it's still a branch of mathematics, but I do not hear much about it anymore. ( Maybe it's just me. )
This branch concerned itself with cutting out parts of a manifold and smoothly replacing them with other parts of a manifold.
A large part of your question relies on the question: "can I preform surgery on spacetime at an event horizon and replace it with some other physically viable interior?".
I think you would get different answers to the question depending on the person:


*

*To a general physicist I think you will get the answer "No."

*To a physicist expert in black hole physics I think you will get the answer "I hope not."

*A mathematician would answer " You probably can."

A: Can we be sure today that we'll never have some sort of faster-than-light travel, some unthinkable technology that transcends spacetime, or some other way that the black hole interior ceases to be unreachable and unknowable?  
A: Well, for one, we could be wrong: perhaps there is a way to "scope" underneath the black hole's horizon, but it seems highly unlikely. Nonetheless, if we find one, we have to revise our understanding and theories accordingly.
But of course, it is entirely logically possible (as demonstrated by the existence of consistent theories where such is true) that there is, in fact, no way, whatsoever, at all, to know empirically and thus it really could be a giant house filled with tiny gnomes.
However, none of those really answer why we'd want to know, only whether or not we can know. The reason why we want to know, I'd say, is because of curiosity. Many, if not most, if not even all, people are curious to at least some degree, though it varies considerably (quite so) from one person to another just how much. This is perennially exemplified by the child for whom being told that a certain closet and/or part of the house is "forbidden" without further explanation by its parents (and/or merely a "pacifying" explanation for which the child instinctively knows is not really the truth), only serves to titillate hir more and more into wanting to get in there and find out what is there, and who may do so or at least try to when parents or others who might deliver reprimand are not present.
And I choose this illustration somewhat carefully, for I feel it is apt: here, the Universe presents us with a similar "closed closet" in the form of a black hole. We want to know what is behind the dang door, darnnit! Open it up and spill the fweaking beans! And if we cannot get behind the door, then we will try and see if there are at least some "sneaky" "breadcrumbs" left behind - hence trying to understand/examine the Hawking radiation: it comes from the black hole after all, so maybe it also has something in it that tells us what is inside. Even moreso, if anything, this particular "closet" seems to be guarded rather closely - its barrier is actually one which in theory does let you in, but it does not let you out again, and once you go in, it condemns one to one's doom! Again, just as with the kid, the harsher the consequences that are threatened for transgressing the pact of secrecy, it is so often the case that hir curiosity cannot help but grow.
A: From my limited understanding of LHC physics, it has not been ruled out that particle accelerators can create subatomic-size objects which would behave very much like black holes, except for the sucking up of matter. Maybe this or other ways of creating black holes on demand could provide limited insight into their inner workings.
A: Yes, the late Polchinski did muse that there's no interior at all, and that everything that ever "fell in" was in fact smeared across the event horizon. Let that be the working assumption here. Then may I propose a test which can be made in the region outside the event horizon to distinguish the "interior / no interior" models?
A careful examination of the gravitational field vectors in the region just outside the event horizon should resolve the issue. The field configuration should differ in the two cases, i.e.
1) A point singularity of mass M centrally located, vs.
2) The same mass M uniformly distributed within a thin shell at the event horizon.
In both cases the vector will point centrally (along a radius vector). However - and please correct me here if necessary -the magnitude of the gravitational attraction will differ in the two cases.
