Why does Mormon specify “exceedingly great faith”? All faith comes as a gift from God, so we are all capable of faith. It is part of our human endowment. But the particular gift here is “exceedingly great” faith. Some have faith so powerful it can move mountains. Obviously, such faith is uncommon, even though we can all achieve some level of faith and improve it. (See commentary on Alma 32.)
A particular subset of God’s gift of faith is the gift of healing. All worthy holders of the Melchizedek Priesthood may participate in blessing the sick, and the power of the priesthood is sufficient for all occasions, depending upon faith. Nevertheless, some have the gift of healing.
Reference: 1 Corinthians 12:9 provides the model for this verse: “To another faith by the same Spirit; to another the gifts of healing by the same Spirit.”