Why doesn’t God heal amputees?

There have been a number of miracles claimed, e.g. someone getting healed from AIDS. Why would God heal those sorts of diseases but not amputees? One factor that's important to recognize is this: AIDS (and other diseases) can be misdiagnosed. Not only is science fallible, but people practicing science are fallible. It is possible to get a false positive on an HIV test, for example. When the person is told they have AIDS, and now it turns out that they don’t, concluding “Miracle!” as opposed to a false positive is the temptation. In contrast, it’s pretty hard to get a false positive on an amputee.

Other claimed healings are those of cancer, but spontaneous remissions have been known to happen. A person might get better from a cold after being prayed for, but the person would have gotten better without prayer anyway. Similarly, it’s not implausible that some people would recover from cancer purely by natural means after being prayed for. Disease is the type of thing that an immune system can fight against, as opposed to a severed limb. People healed of cancer might be tempted to shout “Miracle!” as opposed to crediting the fortunate event to spontaneous remission. In contrast, it's pretty implausible that the immune system would suddenly poof a limb into existence.

So the problem with other healings is this: the evidence is underdeterminative. It isn’t clear that non-divine causes played a role with (for example) cancer, when spontaneous remission is known to happen. And people have been misdiagnosed as HIV positive when a subsequent test answers in the negative, as in the case of Jim Malone. Thus when someone is “cured” of an HIV infection or from cancer, there are non-miraculous explanations. In contrast, if an amputee were suddenly healed after being prayed for, the “Miracle!” explanation would pretty much be the only explanation. Funny how those sorts of miracles are the ones that don’t occur, isn’t it? For the theist who believes that God supernaturally intervenes in the modern world, this should be cause for the theist to reconsider that belief.

Things like a misdiagnosis and a successful immune system wouldn’t apply for such an amputee healing, and the evidence for a miracle would be a lot more determinative. So why don’t we see God perform miracles of this sort? Why doesn’t God perform miracles in cases like these where a miracle would be the only viable explanation of healing, unlike the cases of cancer and a putatively healed HIV infection? Why would God act in such a way that his “miracles” would be indistinguishable from a non-miraculous world of misdiagnosing mishaps and natural healing, as if God weren’t miraculously intervening at all?

One might say “God needs to remain hidden.” This would be problematic for Christian apologists who believe there is strong evidence for their religion. And Christians in general would have to give up the claim that God worked obvious miracles like water into wine, or God raising Jesus from the dead. And let’s not forget the rather impressive supernatural events of the Old Testament such as the proverbial burning bush in the in Exodus 3, or the pillar of fire of Exodus 13:21, or the conspicuous supernatural plagues that God brought upon ancient Egypt in Exodus 7-11, or the parting of the red sea in Exodus 14:21-22—and that’s all just from one book of the Old Testament! So the idea that God wants to remain hidden just doesn’t hold water if the Judeo-Christian God exists. The Judeo-Christian theist is thus in an intellectual hard spot, especially if he or she wishes to claim that God performs miracles today.