Does Matt. present Jesus as the one who perfectly fulfills what Israel should have been? He is the line of David, ch. 1, and the one who exemplifies "God with us," the one to whom the nations come (the magi), who is revealed by dreams (the magi and Joseph have dreams reminiscent of OT Joseph's dream and Daniel's visions[?]), the one called out of Egypt (who exemplifies the New Exodus), the one who is exiled and cried for by Rachel (Jer. 31) the one who is despised (a Nazarene), who then is in the wilderness as the first generation Israelites were yet He overcame temptation successfully.
Does Jesus epitomize New Israel, New Exodus, New Wilderness overcoming, New Exile all in a perfect way?

As Jesus exemplified what God called Israel to be, He is the personification of what triumphing over the world is (Israel over Egypt, Jesus over Herod), New Exodus. Even in the midst of exilic chaos He triumphs (Judah through being exiled to Babylon--Rachel cries for her children, Jesus, whose birth causes many young children around Bethlehem to be killed, yet He escapes), New Exile. Jesus also is tempted in the wilderness for 40 days yet overcomes (Israel tempted 40 years and fails), New Wilderness.

Although New Wilderness is the weakest point because Jesus wasn't being punished as they were, the conclusion of the temptation by Satan has Jesus doing great miracles in Zebulon and Naphtali (Galilee) in fulfillment of Is. 9, which fulfillment is in contrast to Zebulon and Naphtali being the first to experience the Assyrian invasion. Their gloom is turned to light because they are now the first to experience Jesus ministry, New Exile.

Please understand I by no means am trying to posit an allegorical understanding, but examining the biblical theology one.