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.
Jesus status as "anointed", his royal lineage, and his fulfillment of Old Testament prophecy are all clearly implied by Matthews use of the title Son of David at the beginning of his Gospel.
But the exact significance Matthew attaches to the term in the rest of his Gospel is much less clear. Every occurrence of the title outside of Matthews first chapter is in the context of one of Jesus healings: both sets of blind men and the Canaanite woman all call on Jesus as Son of David when they ask him for healing (Matt 9,27; 15,22; 20,30-31), the people ask if Jesus is the Son of David after he heals the blind and mute man (Matt 12,23), and Jesus is acclaimed by the crowds and the children as Son of David before and after he occupies the temple to conduct his healing there (Matt 21,9.15). Matthew clearly associates the title with Jesus as healer30, but why?31.
A reference to David (or his son) could be used to evoke a number of different associations32: the greatest king of Israel, as noted above; a charismatic leader who has the authority to disregard established rules when they do not suit him (Matt 12,1-8); the humbled penitent of 2 Sam 12,1-25; the great poet of the Psalms, wherein he shows his passion for the Lord (cf. 2 Sam 6,14), but which also show him to be capable of predicting the future like a prophet (Matt 22,43)33. None of these, with the possible exception of the last, would carry any association with healing abilities34, but since David was associated with the prophets predictive abilities and not with the miracle-working abilities of prophets like Elijah or Elisha, the necessary connection would not seem to be found there.
If Son of David refers to Davids actual son Solomon, then this too would carry several different associations: the last great king of a united Israel; the great sage and patron of wisdom (Matt 12,42)35; a powerful exorcist and magician36. Again, only the last of these could carry any association with healing; but since we have seen that Matthew deliberately redacts his material to present Jesus more as a healer than as an exorcist, a connection with Solomon would also not seem to be the answer to why he is called Son of David in his capacity as healer.
The answer would seem to lie in Matthews last two stories of Jesus as Son of David and in the Old Testament stories they evoke. As noted,