All attributions are now verified at the source. Here's the research summary.

The question presses precisely because of what John's baptism was. John administered a baptism of repentance in which people confessed their sins as they went into the Jordan (Matt 3:6, 11; Mark 1:4) — and the sinless Son had nothing to confess. John himself saw the problem before anyone else: "I need to be baptized by you" (Matt 3:14). So the whole Reformed tradition treats Jesus' answer in Matthew 3:15 — "thus it is fitting for us to fulfill all righteousness" (πληρῶσαι πᾶσαν δικαιοσύνην) — as the interpretive crux, and its answers unpack that phrase along four convergent lines.

First, obedience — the opening public act of His active obedience. Calvin, in his Harmony, says the general reason Christ received baptism was to render complete obedience to the Father — not a question of rank between Himself and John, but of what their respective callings from God demanded. Gill's Exposition reads the phrase as "it became Christ to fulfil all righteousness, moral and ceremonial," baptism being part of the Father's will He came to do; Matthew Henry stresses that in His estate of humiliation Christ owned every divine institution, and Poole adds that He was baptized not for remission of sins but in obedience to His Father's will. The textual warrant that John's baptism was a divine requirement upon Israel is Luke 7:29–30 — refusing it meant rejecting God's purpose. Sproul draws the doctrinal payoff explicitly into the obedientia activa: Christ had to keep every stipulation the Lord gave His people in order to secure a perfect righteousness for us, and had He neglected this command His obedience would have been deficient — our salvation required His obedient life, not His death alone. Sproul ties Christ's active obedience directly to the baptism narrative in his Luke exposition.

Second, identification — the sinless One numbered with transgressors. Ferguson (Ask Ligonier, "Why Did Jesus Have to Be Baptized?") presses the visual logic: the Jordan water was symbolically laden with the confessed sins of the people; in receiving that water Jesus performed a prophetic act pointing to the cross — He would later call the cross the baptism still awaiting Him (Luke 12:50) — being, in Ferguson's words, "baptized into our sin in order that we might be baptized into His righteousness". Ligon Duncan makes the same move: Christ was baptized for us, yet not repenting for us — the rite signified His willing acceptance of the Mediator's humiliation, taking whatever abasement was necessary to save His people. This is the vicarious strand: Isaiah's Servant "numbered with the transgressors" (Isa 53:12), with the Father's voice at the Jordan widely recognized as fusing Psalm 2:7 (royal Son) and Isaiah 42:1 (Servant) — kingship and sin-bearing announced in one breath. Spurgeon's Baptist reading belongs here too: he explicitly denies that the rite itself fulfilled all righteousness — the baptism was "a picture or emblem of the fulfillment of all righteousness", and the dying, burial, rising, and ascension it depicted are what actually fulfill righteousness and save sinners — Christ's "baptism of blood," not our water.

Third, inauguration — Messianic anointing and Trinitarian attestation. The Christ is the Anointed One, and the Jordan is where the anointing happened. Calvin reads the Spirit's descent through Isaiah 61:1: at His thirtieth year Christ was introduced by baptism into His public office as Redeemer and clothed with the Spirit's power for it (the apostolic gloss is Acts 10:38). Sproul stresses that it is the human Jesus who is anointed by the Spirit for the Messianic mission; Ferguson calls the baptism His public emergence — the transition point of redemptive history, John having come baptizing precisely so that Christ might be revealed to Israel (John 1:31) — with a fresh anointing whose dove-imagery echoes both the flood and the creation, signaling the work of new creation now beginning. MacArthur's well-known framing of Matthew 3:13–17 is in this key: "This is, as it were, His coronation" — His commissioning, the beginning of His ministry. And Matthew Henry notes the Trinitarian manifestation: the Father confirming the Son as Mediator, the Son solemnly entering the work, the Spirit descending to be communicated through His mediation to His people.

Fourth, consecration of the ordinance — and union with Christ. This is Calvin's "special reason," and it lands squarely in your Baptized into Christ project: Christ received the same baptism as we do to assure believers they are ingrafted into His body, buried with Him in baptism to rise to newness of life (Calvin cites Romans 6:4 here directly), the particular purpose being that He would "consecrate baptism in his own body" so that we might have it in common with Him. Gill draws the same application: since baptism became Christ, it cannot be unbecoming for His followers, and ought to be attended to by all who would be counted His. Ferguson elsewhere summarizes the heart of it: baptism signifies union with the Christ who was made sin for us that we might become the righteousness of God in Him.

Through your redemptive-historical lens, the strands cohere further: Matthew has already established the Son-as-true-Israel pattern (Hos 11:1 in Matt 2:15), and the sequence — through the waters, then forty days in the wilderness answering Israel's forty years, answering the tempter from Deuteronomy — presents the baptism as Israel's history recapitulated in her faithful Head. That typology is warranted by Matthew's own structure; the further Jordan-conquest resonance sometimes preached is best labeled constructive rather than exegetically demonstrated.

Two divergences worth flagging for your files. On the scope of "all righteousness": Gill, Henry, and Poole read it as conformity to every divine requirement; Calvin explicitly considers the law-keeping reading but prefers a simpler appeal to their God-given callings; Spurgeon relocates the fulfillment from the rite to the redemptive work it pictures. And Calvin insists John's baptism and Christian baptism are one in meaning, power, and substance — a claim with obvious bearing on how directly Christ's baptism warrants the church's ordinance, and one Reformed Baptists have handled with varying degrees of sympathy.

The one-sentence synthesis: Jesus was baptized not to be cleansed but to obey, to identify, and to be installed — the sinless Son submitted to a sinners' baptism as the first public act of the obedience He would render for His people, was thereby numbered with the transgressors He came to save in a sign anticipating His cross-baptism, was anointed by the Spirit and attested by the Father as Messiah at the threshold of His ministry, and in going down into the water consecrated the ordinance that now signifies His people's union with Him in His death and resurrection.

Per the truth protocol: every named attribution above was verified this session against the linked sources (Calvin's Harmony via the CCEL text, Gill's Exposition, Spurgeon's "Lessons from Christ's Baptism," and the Ligonier, FPC Jackson, and MacArthur-excerpt pages); the Psalm 2:7/Isaiah 42:1 blend and the true-Israel typology are presented as broad scholarly consensus and canonical-structural argument respectively, not pinned to an individual. The final synthesis paragraph is my own construction from these verified positions. If you'd like, I can build this out as a Modern Minimalist source survey on Matthew 3:13–17 — parallel to your Romans 6:3–4 survey, with a full source-location table and a Logos Notes variant — as a companion to Baptized into Christ.