I'm not sure any disease is "meant" to be cured. The fact that we can cure any diseases at all is a lucky accident.

Is this a religious conviction, or something else? I've heard that viewpoint a lot, but I've never heard anyone really explain where it comes from.

Smallpox was not meant to be cured anyway, but we did, and we're better for it. One of the defining qualities of humanity is the ability to better ourselves and overcome challenges.