Christ fully paid the debt of our sin and is now sitting at the right hand of God. He can relate to us in our sinful condition because He took on human flesh. He identified Himself with us. Christ forever makes intercession on our behalf before the Father (Hebrews 4:14-16; 7:23-28).
His Mediatorship is superior to that of the Old Testament. It is eternal. It is permanent. His role is a replacement of the Old Testament priesthood. We can approach God with confidence through Christ's body and shed blood (Hebrews 10:19-23). We obtain grace and mercy in times of need.
If Jesus Christ is the one and only qualified Mediator because of His sacrificial work on the Cross, then any potential mediatorial position of Mary would be redundant. The position of mediator and intercessor is exclusive to Him. He is sufficient to bring about all things pertaining to our redemption.