While not to diminish what SpaceX has achieved it's really a far cry from "curing cancer".
While what they've done too allot of engineering it's not nearly as complex as identifying all of the biological pathways for even a single form of cancer and finding a reliable cure.
That said we do have good treatments for the vast majority of forms of cancer, the problem is that your survivability is directly tied to how early it's detected, surgical removal, radiation and more notably modern chemo regiments are very effective in early stages of detection.
Many type of cancer today have 90%+ survivability rates if they are detected early enough, detection isn't always easy allot of them can not turn symptomatic till later stages, and many of them won't show up in blood work / body scans clearly either.
