The Levitical priesthood was only necessary for a period of time until the Melchizedekian priesthood was fulfilled in Christ. The lesser priesthood (and the lesser covenant) are no longer needed! Why have the Mosaic Law at all?!?
The Levitical priesthood and its related sacrifices were unable to remove sin, cleanse the conscience, or purify the heart (Hebrews 10:4). But that's OK because it was never intended to do those things. The Levitical priesthood had a different purpose than the Melchizedek priesthood.
The "order" of Melchizedek is not some type of monastic society or secret order, it is a sequential order... a sequence or an array. The the order/sequence of Melchizedek began with Adam. The title (Melchizedek/my king is righteous) was his until he died and then the title was passed sequentially from father to son (or grandson) down through Abraham, Isaac, Jacob, Judah, King David, King Solomon, and so on, until it came to Christ. Because Jesus was resurrected, never to die again, the title of "Melchizedek" is His forever. The whole reason the "order of Melchizedek" is so important is because it culminates in Christ! For more information about Melchizedek check out this article entitled The Mystery of Melchizedek on Psalm11918.org.
As far as the second question "Why have the Mosaic Law at all"?
It should be noted that there is nothing wrong with the Mosaic Law. It has multiple purposes: when God's Law is broken then it reveals humanity's sinful nature (Romans 3:20). When His Law is obeyed then it demonstrates the God's wisdom (Deuteronomy 4:5-8) and His righteousness (Isaiah 42:21) and holiness (Romans 7:12). But God's Law cannot redeem humanity or bring about salvation. That was never its purpose.
The writer of the letter to the Hebrews makes the point that Christ's work in the Melchizedek priesthood is greater than the work of the Levitical priesthood.
The Levitical priesthood and its related sacrifices were unable to remove sin, cleanse the conscience, or purify the heart. It was never intended to do those things. The Levitical priesthood had a different purpose: point to the Messiah and the need for a Redeemer.
Jesus' priesthood and His sacrificial work was able to remove sin, cleanse the conscience, and purify the heart. As Hebrews 7:28 says, "For the Law appoints men as high priests who are weak, but the word of the oath, which came after the Law, appoints a Son, made perfect forever."
Christ's work in redeeming humanity from their sins is a far greater thing than the Levitical priesthood's work in pointing out the need for such a redemption.
Why have the Mosaic Law at all? The world still needs to understand the wisdom of God. We still need to see God's righteousness and holiness lived out in a real and tangible way. And, until Yeshua returns, humanity still needs something to remind us of our sin and our need for Jesus the Christ, our Redeemer.