Actually, he does. Most assuredly. It is a cardinal article of our faith.

I know that my redeemer lives,
and that in the end he will stand on the earth.
²⁶ And after my skin has been destroyed,
yet in my flesh I will see God;
²⁷ I myself will see him
with my own eyes—I, and not another.
How my heart yearns within me!
–Job 19:25-27, NIV

No illness, in other words, can ultimately endure his return in final glory. The day will come when he dries every tear and grants us new and perfect bodies, as well as a new heavens and a new earth in which we will dwell forever in his presence. When that will happen, we know neither the day nor the hour.

But our hearts ought to yearn for it unceasingly.

What we really mean when we ask why God doesn’t heal everyone is, “Why doesn’t God heal everyone right when they ask, precisely in the way that they desire?”

For the answer to that question, I commend to you the rest of the Book of Job. Just be prepared for God to ask a challenging question or two of his own in the process.

Who is this that darkeneth counsel by words without knowledge?
—Job 38:2, KJV