Could the point the writer in Hebrews is making be that there is no mention of Melchizedek's genealogy in the OT? He obviously represents Messiah as Hebrews 7 explains. His Name means King of Righteousness and He is King of Salem or King of Peace. Yet He is also a Priest. Messiah is King of Righteousness and King of Peace and our High Priest in the order of Melchizedek. He is King and High Priest because of what He did to save us and Who He is.
Hebrews 2
13 Again, “I will put My trust in Him.” Again, “Behold, here I am with the children whom YAH has given Me.” 14 Since then the children have shared in flesh and blood, He also Himself in the same way partook of the same, that through death He might bring to nothing him who had the power of death, that is, the devil, 15 and might deliver all of them who through fear of death were all their lifetime subject to bondage. 16 For most certainly, He doesn’t give help to angels, but He gives help to the offspring of Abraham. 17 Therefore He was obligated in all things to be made like His brothers, that He might become a merciful and faithful High Priest in things pertaining to YAH, to make atonement for the sins of the people. 18 For in that He Himself has suffered being tempted, He is able to help those who are tempted.