That reminded me of the last Priest prior to the destruction of the Temple itself, who was utterly unfit for the position. From Wikipedia, which quotes Josephus:
"Phannias ben Samuel (in Hebrew: פנחס בן שמואל Pinhas ben Shmuel) (c. 70 CE) was the last Jewish High Priest. He did not originate from a priestly family but was the leader of revolutionary forces. He died during the destruction of Herod's Temple in 70 CE.
In order to see how far their power extended, the Zealots
'...undertook to dispose of the high priesthood by casting lots for it, whereas, as we have said already, it was to descend by succession in a family. The pretense they made for this strange attempt was an ancient practice, while they said that of old it was determined by lot; but in truth, it was no better than a dissolution of an undeniable law, and a cunning contrivance to seize upon the government, derived from those that presumed to appoint governors as they themselves pleased. Hereupon they sent for one of the pontifical tribes, which is called Eniachim, and cast lots which of it should be the high priest. By fortune the lot so fell as to demonstrate their iniquity after the plainest manner, for it fell upon one whose name was Phannias, the son of Samuel, of the village Aphtha. He was a man not only unworthy of the high priesthood, but that did not well know what the high priesthood was, such a mere rustic was he! Yet did they hail this man, without his own consent, out of the country, as if they were acting a play upon the stage, and adorned him with a counterfeit thee; they also put upon him the sacred garments, and upon every occasion instructed him what he was to do. This horrid piece of wickedness was sport and pastime with them, but occasioned the other priests, who at a distance saw their law made a jest of, to shed tears, and sorely lament the dissolution of such a sacred dignity.[1]'"
Notice Josephus explains it is from "descent in family." They just don't go up to some random Levite and give him the high priesthood. It is inherited. That sheds even more light on the meaning of the phrase in the scripture from Hebrews, "an unchangeable priesthood... by the power of an everlasting life." Since Jesus cannot die, the Priesthood cannot be inherited by anyone else. It is the everlasting Priesthood of our one and only High Priest. Just as Melchizedek has no record from whence he came, or where he went.
The Mormon practice of many Melchizedek holders, including many Aaronic Priesthood holders who do not even perform the duty of Priests, has no basis in Old Testament or even New Testament teaching.