I think this is important on the grand scheme of things if this person's identity is taken to mean something scripture does not say. Simply put, Melchizedek is not Jesus. He was a real priest and king of a particular place called Salem (peace). The place where Abram rescues lot is located near what came to be known as Jerusalem (peace). Melchizedek is a type of Christ, but not God Himself. NO worship is ascribed to Melchizedek, but he is just simply a type or figure of Christ just as Moses was likened unto as a prophet. Yet, Moses was not Christ. Another thing is that we never see Melchizedek associated with "the angel of the Lord, an angel of the Lord, the captain of the host of the Lord, etc.", who although does not have a distinct identification is a theophany and accepts worship. We do not see Melchizedek represented in such a way.

There is no way, without stretching the language out, that Melchizedek can be Jesus. He was made "LIKE" unto the Son of God, Jesus was the Son of God. Melchizedek's name was "INTERPRETED" king of righteousness, king of peace. Jesus actually was both. So it is the characteristics of him , not the person of Melchizedek that are important.

P.S. There was no record of who his parents were, but Melchizedek had parents (his genealogy). There is no record of his birth or death, but both happened. Well let's look at Jesus. He was born, we know his genealogy (which contains no earthly physical father), and we know He died, yet He lives. SO they share similarities, but they are not one in the same.