We now get to the real reason that Alma brings up Melchizedek. Alma wants to use Melchizedek as an example of a righteous leader whose people who have gone astray. This story is not in either the Old or the New Testament but was apparently on the brass plates. Alma is not preaching about priesthood here, even though the text resembles Hebrews. Alma is making an argument for the Atoning Messiah and for the necessity of repentance. In fact, all of his arguments are shaped toward that end, including his discussion of priesthood.
In this case, he again appeals to the ancient as a model for the present. Melchizedek was a righteous leader with a wicked people. Alma is a righteous leader (and not coincidentally, a priest after the order of Melchizedek) and the Ammonihahites are a wicked people.