In his commentary on Gen 14, John Calvin gave the following reasons for
rejecting the common identification of Melchizedek with Shem; while I am not
dogmatic about it, I actually agree with Calvin (shocking, I know!) and others who reject this
identification as "improbable":
[M]any imagine
Melchizedek to have been Shem; to whose opinion I am, for many reasons,
hindered from subscribing. For the Lord would not have designated a man, worthy
of eternal memory, by a name so new and obscure, that he must remain unknown.
Secondly, it is not probable that Shem had migrated from the east into Judea;
and nothing of the kind is to be gathered from Moses. Thirdly, if Shem had
dwelt in the land of Canaan, Abram would not have wandered by such winding
courses, as Moses has previously related, before he went to salute his
ancestor. But the declaration of the Apostle is of the greatest weight; that
this Melchizedek, whoever he was, is presented before us, without any origin,
as if he had dropped from the clouds, and that his name is buried without any
mention of his death. (Heb 7:3). But the admirable grace of God shines more
clearly in a person unknown; because, amid the corruptions of the world, he
alone, in that land, was an upright and sincere cultivator and guardian of
religion. I omit the absurdities which Jerome, in his Epistle to Evagrius,
heaps together; lest, without any advantage, I should become troublesome, and
even offensive to the reader. I readily believe that Salem is to be taken for
Jerusalem; and this is the generally received interpretation. If, however, any
one chooses rather to embrace a contrary opinion, seeing that the town was
situated in a plain, I do not oppose it. On this point Jerome thinks
differently: nevertheless, what he elsewhere relates, that in his own times
some vestiges of the palace of Melchizedek were still extant in the ancient
ruins, appears to me improbable.