Charles-Edward Amory Winslow (The Conquest of Epidemic Disease: A Chapter in the History of Ideas, pages 36-37) explains How the ancient Israelites viewed the occurrence of disease:
Among the Semitic peoples, the concept of disease as punishment for sin reaches its apogee ... In sharpest contrast with the prevailing demonology of the New Testament, as well as with Babylonian and Persian ideology, the overwhelming mass of references to disease in the Old Testament, from beginning to end, involve the higher concept of punishment for sin and the nobler gospel of righteousness as its only remedy.
In that context, Exodus 15:26 does not just promise supernatural healing or that obedience to the Torah would bring health, as we understand health today. Instead, this passage promises that God will not inflict disease on those who obey him. A parallel passage in Deuteronomy 7:15 does more clearly suggest supernatural healing, but once again the promise is that God will not inflict disease on those who obey him.
Deuteronomy 7:15: And the LORD will take away from thee all sickness, and will put none of the evil diseases of Egypt, which thou knowest, upon thee; but will lay them upon all them that hate thee.