Healing the sick, feeding the hungry, and raising the dead were good deeds in and of themselves, but the purpose of doing those things was not the good that He could do for men. The PURPOSE of those acts was to prove that He was who He said He was. It is demonstrated in at least two places that the Jewish leaders of the day knew this fact.
John 3:1 and following shows Nicodemus coming to Jesus and saying that I know you are from God, because no one can do what you have done except for God being with him. Because of what you have done, I know your message is from God.
John 6:30 the Jewish leaders ask Jesus point blank, you say you are from God, but what sign will you do to prove it. A messenger from God (in that day and time) could do signs and wonders on demand to prove his message's validity. If he could not do the sign on demand, he was a fake and was to be killed.
Today, no one can do signs and wonders "on demand", because we have the Word written down with proofs both within it, and in the secular history that back up the validity of the written Word. There is no more Biblically defined need for miracles today.
Matthew 10:8 Heal the sick, cleanse the lepers, raise the dead, cast out devils: freely ye have received, freely give.
This is the comission Jesus gave to His disciples as we read in Matthew 28:18-20 as they went out to the nations making disciples of all who would accept the word of God.
Mark 16:14 Afterward he appeared unto the eleven as they sat at meat, and upbraided them with their unbelief and hardness of heart, because they believed not them which had seen him after he was risen. 15 And he said unto them, Go ye into all the world, and preach the gospel to every creature. 16 He that believeth and is baptized shall be saved; but he that believeth not shall be damned. 17 And these signs shall follow them that believe; In my name shall they cast out devils; they shall speak with new tongues; 18 They shall take up serpents; and if they drink any deadly thing, it shall not hurt them; they shall lay hands on the sick, and they shall recover. 19 So then after the Lord had spoken unto them, he was received up into heaven, and sat on the right hand of God. 20 And they went forth, and preached every where, the Lord working with them, and confirming the word with signs following. Amen.
Miracles and healing are for today just as they were when Jesus walked the earth during His ministry showing signs and wonders of God's mercy and grace. These are a part of the Spiritual gifts, 1 Corinthians 12:27-31, given to the members of the body of Christ who are indwelled with the Holy Spirit through the Spiritual rebirth from above where Christ sits at the right hand of the Father making intercession for us, Romans 8:34. John 3:5 never mentions the word baptize, but says only by being born of water and spirit, which means water as living water (word of God) that no one can enter into the kingdom of God unless they are Spiritually renewed (born again) by the hearing of the word, which is Christ Jesus and by the Holy Spirit that came on them in the OT and indwells us as taught in the NT. Many do read into the passage a preconceived idea or theology, but baptism is never mentioned in this verse. Word is living water as described in John 4:10; 7:38; 1 John 5:6; Jeremiah 2:13; Isaiah 55:1-3 to name a few.
Messengers are created angels of God being spirit beings as Jesus was not a messenger of God or a created spirit of God, but the Son of God in whom God gave all power and authority, Matthew 28:18. Jesus never spoke apart from that which God gave Him to speak, John 12:49, 50. No messengers, being angels of God, can do anything on demand by others as God gives them what to do or what to speak. Hebrews 1:1-14 teaches us the supremacy of God's Son being made so much better than the angels who are God's messengers.
Jesus never baptized anyone in literal water that we know of and also instructed the Disciples to wait upon the indwelling of the Holy Spirit, Acts chapter 1, and then commissioned them to go out preaching the Gospel (word/living water) and to baptize in the name of the Father, Son and Holy Spirit, Matthew 28:16-20.
Being born from above means being born from the heavenly word of God, not dirty river water. When Jesus was baptized by John it was for the fulfillment of Messiah come as the Holy Spirit fell down on Him. Jesus had no need of being baptized in water for the remission of sin.