One of the arguments you use that Jesus was willing for us to be healed was when the man asked “Lord, if you are willing…” in Mathew 8:1-3 and the Lord’s answer was “I am willing”.
However, it seems the Lord was not always willing in all cases. For instance concerning the Cananite woman in Mathew 15:22-28. Even though in the end he does heal her daughter, at first He was reluctant. Would this reluctance continue with all gentiles, or was this limited only to his earthly ministry before his death and resurrection?
At this point in His ministry, Jesus was focused on the Jews. To fulfill a promise God had made to Israel, they had to receive a bona fide offer of the Kingdom and reject it before the door could be opened to the Gentiles. When He first sent the disciples out, He told them to only visit Jewish communities. (Matt. 10:5-6)
That’s why in the conversation with the Canaanite woman Jesus said He was only sent to the lost sheep of Israel. He called the Israelites “the children” and Himself “the children’s Bread”. The woman understood this and compared her daughter and herself to the children’s dogs and the crumbs that fall from the table to a part of the children’s bread (Him) that they would never miss. In other words, if He healed her daughter it wouldn’t really deprive the Jews of anything, because it would be such a small thing for Him. It was this declaration of faith that impressed Him.
Once Israel had rejected His offer (as He knew they would) the door was opened to the Gentiles and since then the opposite has been true. The Church has been blessed far beyond anyone’s expectations partly for the purpose of making Israel jealous (Romans 11:11) and there is no longer any reluctance on the Lord’s part to bless us us with every spiritual blessing (Ephesians 1:3).