Why Jesus Healed Some
Matthew 1-10 follows the Dominion pattern. After Jesus’ testing in the wilderness, in 4:18-8:13 Jesus called His disciples and began mustering a new holy army – the “next generation”. It was reported to Him that the last Old Covenant Nazirite (holy warrior) was dead. It was time for new warriors. Jesus healed the uncleanness of many, creating a new priesthood. His success in the wilderness as a new Head made possible this new body. Peter Leithart writes:
By my count, there are twelve disfigurements listed in Leviticus 21:18-20 that disqualify a priest from serving at the altar and in the tabernacle: blind, lame, slit, deformed, broken foot, broken hand, hunchback, dwarf, defect of eye, eczema, scabs, crushed testicles. The listed disfigurements point to a disfigured Israel, twelve disfigurements for twelve tribes. And this adds some depth to the fact that Jesus heals many of these disfigurements as He creates a new Israel. 
There was not one factor that could possibly make a child of Adam unfit to serve in this new Tabernacle. Everyone could be made an acceptable sacrifice in this new High Priest. Yet, not everyone was chosen.
After this Trumpets section, 8:14 to 9:8 concerns Atonement, so Matthew quotes Isaiah to support his presentation of Christ as High Priest, carrying the sins of Israel:
This was to fulfill what was spoken by the prophet Isaiah: “He took our illnesses and bore our diseases.”
After Jesus making the storm tossed sea into a sea of glass (the Laver, the veil), the Atonement symbols continue with demoniacs living among tombs (the Most Holy Place). Jesus symbolically took their nakedness. The demons, as the second goat, were expelled into a herd of unclean beasts (pigs) which attempted to cross the sea but were drowned. These two pictures present Christ as a boat, the ark of Noah that brings resurrection to Greater Eve but condemns the legions of the unclean.  He crossed the sea twice perhaps because the High Priest approached the Most Holy twice: once for the priesthood and once for the people.
 The sermon on the mount within this structure of chapters 1-10 is “Deuteronomic.” Jesus “received” the Law from the Father as He ascended from the waters of baptism, and now repeated it to a new Israel to prepare them for conquest.
 Disfigured Israel
 Cobbled together from bits of Totus Christus chapter 26. Read the intro and chapter 1 here (PDF).