I don’t think this is true.
Here's why: If God is an all-good God, He would want what is best for humanity. If what is best for humanity, according to an all good God, is for humans to enjoy a peaceful everlasting life, filled with love and meaning, then God would want that for humanity, even if that comes with imperfect health. This suggests that God logically must provide a way for humans to engage freely into a loving relationship with Himself, or he would not be all-good. However, God is all-good and morally perfect by definition.
Okay, so now suppose that God created human beings impervious to disease or injury. We as humans would not need any saving at that point. In essence we would be our own providers, rulers, and maybe even gods ourselves. Humans would feel no need to enter freely into a relationship with God; after all, they are basically gods and don’t need any help from anyone else. If this were to be the case, then humans would not have a way to enter into a relationship with God because they would be blinded by their own perfection, thus, they would not be able to reach what is best for humanity according to God.
God, logically, can’t NOT provide a way to give humanity an opportunity to attain what is best for humanity because he is all-good, and that is exactly what would happen if humans were impervious to disease or injury, therefore, God can’t, logically, create humans impervious to disease or injury. It is impossible.
Since the first premise in the original argument is false, it makes the whole argument reliant on a faulty premise which makes the argument unsound.