Sovereign God heals in any way he chooses

And they came to Bethsaida. And some people brought to him a blind man and begged him to touch him. And he took the blind man by the hand and led him out of the village, and when he had spit on his eyes and laid his hands on him, he asked him, “Do you see anything?” And he looked up and said, “I see men, but they look like trees, walking.” Then Jesus  laid his hands on his eyes again; and he opened his eyes, his sight was restored, and he saw everything clearly.
—Mark 8:22-25

J. C. Ryle comments on this passage:

We do not know the reason of the peculiar means employed by our Lord Jesus Christ, in working the miracle recorded in these verses. We see a blind man miraculously healed. We know that a word from our Lord’s mouth, or a touch of His hand would have been sufficient to effect a cure. But we see Jesus taking this blind man by the hand–leading him out of the town–spitting on his eyes–putting His hands on him, and then, and not until then, restoring his sight. And the meaning of all these actions, the passage before us leaves entirely unexplained.

But it is well to remember, in reading passages of this kind, that the Lord is not tied to the use of any one means. In the conversion of men’s souls there are diversities of operation, but it is the same Spirit which converts. So also in the healing of men’s bodies there were varieties of agency employed by our Lord, but it was the same divine power that effected the cure. In all His works God is a sovereign. He gives no account of any of His matters.