"There is a tendency in German homiletic literature, and in the commonly accepted approach to this text, to see the desire to build three huts as an expression of Peter's sense of well-being; and this in sharp contrast to the Passion that is now beginning. But this cannot be the case: the voice from heaven must be understood rather as a sharp correction of precisely this statement from Peter. The point of Peter's 'uncomprehending' answer is revealed clearly in the complete equality with which he treats Jesus, Moses, and Elijah. If each one of them receives a dwelling, then these three authorities will live and speak, teach and die, next door to one another in three similar houses of instruction. For the 'tent' or 'hut' or 'house' or 'dwelling' is not intended for their private lives, but rather as the place for receiving revelation and for an enduring and repeated encounter with God, as was the tent of Moses during the Exodus from Egypt. It is only from this perspective that the statements make sense.
"The meaning of the heavenly voice's correction, then, is this: only the Son, only Jesus Christ is appointed mediator between God and man. Only he speaks legitimately about God. And when the voice from heaven says, 'listen to him,' then this also means that Jesus is the one who legitimately interprets the entire revelation of Scripture, of the Old Testament", Law (Moses) and Prophets (Elijah) alike.
Klaus Berger, "The Transfiguration of Jesus," trans. Nicholas J. Healy III, Communio: international Catholic review 35, no. 1 (Spring 2008): 76-77, emphasis mine. The reference is to Mk 9:5-8 and parallels. Interesting, then, that in Luke Peter says this "as [Moses and Elijah] were parting from [Jesus]", almost as if to keep them there! (The Synoptics, by contrast, are careful to stress that the disciples are left with "Jesus only" (Mk 9:8, Mt 17:8; Lk 9:36).)