Notice how the two healings which include the use of "Son of David" involve two blind men each. There is a reason there are two occasions involving this healing, but we will just look at them in the big picture.
"When Jesus departed from there, two blind men followed Him, crying out and saying, “Son of David, have mercy on us!” And when He had come into the house, the blind men came to Him. And Jesus said to them, “Do you believe that I am able to do this?” They said to Him, “Yes, Lord.” Then He touched their eyes, saying, “According to your faith let it be to you.” And their eyes were opened."
"And behold, two blind men sitting by the road, when they heard that Jesus was passing by, cried out, saying, “Have mercy on us, O Lord, Son of David!” Then the multitude warned them that they should be quiet; but they cried out all the more, saying, “Have mercy on us, O Lord, Son of David!” So Jesus stood still and called them, and said, “What do you want Me to do for you?” They said to Him, “Lord, that our eyes may be opened.” So Jesus had compassion and touched their eyes. And immediately their eyes received sight, and they followed Him."
The two blind, I believe, represent the two kingdoms in Israel. The kingdoms were united under the physical son of David, Solomon, and will be again under the second "Son of David," Christ.
"Behold, the days are coming, says the Lord, when I will make a new covenant with the house of Israel and with the house of Judah..."-Jer 31:31 (Heb 8 )
Notice the Lord responds immediately to their cries. However. there is one other "Son of David" plea in Matthew, but here he ignores the cry, and eventually calls the one making the plea a "dog."
"And behold, a woman of Canaan [gentile] came from that region and cried out to Him, saying, “Have mercy on me, O Lord, Son of David! My daughter is severely demon-possessed.” But He answered her not a word. And His disciples came and urged Him, saying, “Send her away, for she cries out after us.” But He answered and said, “I was not sent except to the lost sheep of the house of Israel.” Then she came and worshiped Him, saying, “Lord, help me!” But He answered and said, “It is not good to take the children’s bread and throw it to the little dogs.”
The Lord is not a liar. He was, indeed, sent only to the house of Israel. But her plea was eventually heard and answered. but only when she dropped "Son of David" and used only "Lord." She was a gentile. He is her God, but not part of the promise of the earthly kingdom. Remember, there is only one way to life in scripture (by grace through faith), but different callings and hopes.
We've noted in the past that we don't need a "harmony" of the gospels, but rather a disharmony. That is, we must compare the things that differ again. Matthew starts off uniquely:
"The book of the genealogy of Jesus Christ, the Son of David, the Son of Abraham"
Here is the Lord's two-fold ministry in Matthew. He is the son of David (Solomon, king over a united Israel, a man of peace) and the son of Abraham (Isaac, the son of promise). In David, Israel would have her kingdom. In Abraham. blessing would come to the gentiles through Israel.
"since Abraham shall surely become a great and mighty nation, and all the nations of the earth [gentiles] shall be blessed in him"
Entry into the earthly Kingdom runs through the book (as we saw in the Parable of the Ten Virgins and the parables of Matthew 13).
This is the framework of Matthew and the parables must be understood in this context. Trying to cram in the gospel of grace or trying to apply kingdom conditions to the Body will only lead us into grave error... and it has for many.
How many unfortunate souls have been enslaved by The Parable of the Talents or The Parable of the Sheep and Goats? Or fooled into thinking they have pleased God's wrath on sin by the works of the flesh?
The three parables of Matthew 25 nowhere mention the death or resurrection of the Lord. They know nothing of blood sacrifice. Because they do not address the gift of life directly.
As we look at these parables, we will find freedom in understanding them in context. Freedom from fear and/or freedom from pride.
We see two gentiles healed in Matthew, neither sees the Lord and he touches neither of them. We see two great expressions of faith from gentiles. So what is the reward for the faith of gentiles in that age? We get an answer from the malefactor on the cross in Luke (the gospel of Paul in the Acts). He asks the Lord, “Lord, remember me when You come into Your kingdom.” (Luke 23:42). Notice again "LORD" from a gentile. The Lord ignores his reference to the Kingdom and promises him future access to "Paradise." "And Jesus said to him, 'Assuredly, I say to you today, you will be with Me in Paradise.'" (v.43). Paradise is a specific hope. It is the location of the Tree of Life. No one currently has access to it. The gift of life is, as it has ALWAYS been, available to all sons of Adam... but there are hopes, rewards, promises, prizes, blessings, etc that vary from one called-out group to another.