My understanding of
Matthew 3:13-15 is that here we see something of an exclamation by John concerning his perception of own unworthiness and helplessness to do anything that would "save" himself. I don't think Matthew intends for us to see John's words here as a teaching; rather they are an expression of emotion and faith; a sort of rhetorical statement by John.
John's baptism was a "baptism of repentance
for the remission of sin..." (
Mark 1:4;
Luke 1:77,
Luke 3:3 and others). John's apparent incredulity was caused by the fact that Jesus came to be baptized by John when Jesus had no sin. Jesus instructs John that His request did not involve sin, but righteousness. Baptism itself alone accomplishes no cleansing (
1 Peter 3:21). It signifies the passage into a new life (
Romans 6:4 and
Colossians 2:12) when accompanied by faith. Jesus began His ministry with the "baptism of John" and this event was considered pivotal in the nascent church (
Acts 1:22). Thus, Jesus' baptism shows us (among many other things) that Jesus had surrendered His human will to that of the Father and would embark upon His mission.
John's only "need" for baptism was would have been:
1) To demonstrate a similar purpose,
2) To signify his own repentance and remission of sins had taken place.
Since John was already on his mission he had no need for the life changing event of baptism at the time Jesus approached him. Whether or not he had been baptized earlier is an interesting question. Having been raised in the household of a Jewish priest with access to the temple, John no doubt had gone through the mikvahot or ritual Jewish cleanings which involved immersion in water.
Whether or not John
needed to be baptized (see your reference to
Luke 1:15) had either become moot or already been answered by the time the events described in
Matthew 3 took place. Unfortunately the exact details appear to elude us. Perhaps John being filled with the Holy Ghost from the womb solves some questions concerning his own sin and repentance. The fact that he was a Nazarite (an Old Testament "holy warrior") from birth would seem to indicate that his own mission and new life may have been coincidental to his natural birth.
But my take on John's words are that they are intended as an exclamation of emotion and are not didactic.