First, this was specifically for cleansing after coming into contact with a dead body. With the entire generation age twenty and up dropping in the desert over the next forty years, contact with a dead body was going to become a serious problem in the camp of more than a million people.
If they followed the normal sacrifices associated with becoming unclean, they'd be sacrificing day and night until no animals remained. So in a practical sense, this was a means to provide that cleansing for each instance without requiring individual sacrifices.
So why these particular elements? First, this sacrifice is different in that the blood is burned up with the heifer. The heifer was a direct condemnation of the Egyptian worship of Isis, in the form of a heifer. It was to have never been under the yoke because no sacrifice was acceptable if it had been used for common purposes. Sacrifices were to have been set apart. The cedar signifies the fragrance of an offering as well as looking toward the cross as the ultimate covering for sin. The hyssop was used elsewhere in rituals for cleansing and purification and the scarlet wool may represent both the stain of sin and the blood that purifies us from sin.
"For if the blood of goats and bulls and the ashes of a heifer sprinkled on those who are ceremonially unclean sanctify them so that they are outwardly clean, how much more, then, will the blood of Christ, who through the eternal Spirit offered himself unblemished to God, cleanse our consciences from acts that lead to death, so that we may serve the living God!" Hebrews 9:13-14