Kim Paffenroth, «Jesus as Anointed and Healing Son of David in the Gospel of Matthew», Vol. 80 (1999) 547-554
Matthew handles his material in order to relate Jesus anointing, healing, and his title "Son of David". Matthew does this in order to present Jesus as the uniquely anointed "Christ", the Son of David who has come to heal, and who is in that respect (and others), greater than his father David.
David was the anointed king, but was not a healer: Jesus Christ, the Son of David, is now the final, climactic example of both.