The need for and the very fact of the salvation of man is a demonstration of, a revelation of, the righteousness of God:
For I am not ashamed of the gospel of Christ: for it is the power of God unto salvation to every one that believeth; to the Jew first, and also to the Greek. For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith. - Romans 1:17
Two related questions pertaining to the nature of this salvation as regards it's mechanism are asked after: 1) Must the Savior be a human, and 2) May the savior be merely human. Most specifically, facet 2 is in question but a short proof of the first facet is in order to bring us to the second.
The first facet is most clearly expressed in Scripture using the language of righteousness. Romans 5 is correctly brought into view by OP as Paul continues to reveal God's righteousness in the Gospel.
- v. 12-14 Sin and it's consequent death enter the world through one man and pass to all man through that one.
- v. 15 The free gift is not like the trespass...one trespass brought death to many but the grace of God in Christ abounded the free gift to many.
- v. 16 The free gift is not like the result of the trespass...judgement followed one trespass unto condemnation but a free gift followed many trespasses unto justification.
- v. 17 Death reigns over man through the offence of one but man reigns in life through the righteousness of one.
- v. 18-19 One man's sin made many men sinners and therefore brought condemnation to all and one man's righteousness justified many and brought life.
This passage in Romans has much more to say about the Righteousness of God in dealing with sin than it does about the constituent natures of the two men it juxtaposes. Nowhere is it stated in this passage that Adam was a mere man. That information must be brought in (rightly) from elsewhere. And nowhere is it stated that Jesus Christ was a mere man or needs to be. Adam was a flesh and blood human and so was Jesus Christ.
Romans 5 explains that one sinless man sinned and the righteous reversal of this is one sinless man remaining sinless. Through one man sin entered and through one man sin is put away. Because God is righteous and just there must be a kinsman-redeemer; there must be one who is fundamentally identified with those being redeemed:
Then cometh Jesus from Galilee to Jordan unto John, to be baptized of him. But John forbad him, saying, I have need to be baptized of thee, and comest thou to me? And Jesus answering said unto him, Suffer it to be so now: for thus it becometh us to fulfil all righteousness. Then he suffered him. - Matthew 3:13-15
And so, in order to redeem fallen humanity, one fundamentally identified with humanity needed to come. One born of a woman (as are all men), one born under the law to redeem those under the law (for had Jesus come without the law there would be no identification with those held under it), one unfallen and yet identified in a baptism of repentance with those who are ... all this and more in order to fulfill all righteousness.
The second facet is most clearly revealed in Scripture using the language of debt.
What is owed by the creation to the Creator by virtue of the fact of creation is obedience. Creation is supposed to declare the glory of God. The Creator sustains His creation and nothing is owed by the Creator to the creation as payment for the required obedience for His mercy falls on the just and the unjust:
But which of you, having a servant plowing or feeding cattle, will say unto him by and by, when he is come from the field, Go and sit down to meat? And will not rather say unto him, Make ready wherewith I may sup, and gird thyself, and serve me, till I have eaten and drunken; and afterward thou shalt eat and drink? Doth he thank that servant because he did the things that were commanded him? I trow not. So likewise ye, when ye shall have done all those things which are commanded you, say, We are unprofitable servants: we have done that which was our duty to do. - Luke 17:7-10
But there are wages owed by the Creator to the creation for disobedience:
For the wages of sin is death - Romans 6:23a
Sin creates a debt or deficit of righteousness in relation to God. Obedience is owed and the opposite is offered. This is seen clearly in the Lord's prayer:
And forgive us our debts, as we forgive our debtors. - Matthew 6:12
And especially clearly in Jesus' parable of the unmerciful servant.
One sin is enough to indebt us to God and incur a wage of death (the soul that sins it shall die) but it also appears that this debt is cumulative as suggested by the fact that the King in the parable took account of all his servants. That he found one with a massive debt indicates there were others found with other amounts. Also leading to this conclusion are the servants variously beaten with few stripes or many stripes:
And that servant, which knew his lord's will, and prepared not himself, neither did according to his will, shall be beaten with many stripes. But he that knew not, and did commit things worthy of stripes, shall be beaten with few stripes. For unto whomsoever much is given, of him shall be much required: and to whom men have committed much, of him they will ask the more. - Luke 12:47-48
And the summary statement of Jesus regarding the woman who anointed his feet makes little sense apart from a notion of accumulated debt:
Wherefore I say unto thee, Her sins, which are many, are forgiven; for she loved much: but to whom little is forgiven, the same loveth little. - Luke 7:47
The principle of righteousness states that some man must remove another man's introduction of a foreign disposition into humanity. God is righteous...a man did it so a man must undo it. Focusing on this aspect alone it is perhaps possible that a merely human and perfect Jesus could reverse the effects of a merely human Adam if what were being considered were simply a reversal in principle. But sin also incurs debt and what is not possible is for a mere man to give God a ransom sufficient to pay the accumulated debt of every human being who ever lived. It is this understanding that lies behind the following from Psalm 49:
Truly no man can ransom another, or give to God the price of his life, for the ransom of their life is costly and can never suffice, that he should live on forever and never see the pit. - Psalm 49:7-9
If a mere man can not pay the accumulated debt owed to the Creator for even one other man's life it is far beyond impossible for a mere man to pay the accumulated debt of all men.
The language of debt is carried all the way through to Christ's last words: "it is finished". The debt which no mere man could repay is discharged by someone greater than a mere man who has come. Someone whose own life is more valuable than the sum of all other lives because He is the source of all life. Someone whose life is a more than sufficient ransom for all. He was with God in the beginning and He was God.
The Word was made flesh and dwelt among us we have been told. Interestingly was made is middle deponent in voice (which indicates that the subject performs the action, instead of receives it) and dwelt among us is active in voice (which also indicates that the subject performs the action, instead of receives it). The Word who was God made Himself flesh and caused Himself to dwell amongst us.
The only ministry we have is the ministry of God's reconciliation:
And all things are of God, who hath reconciled us to himself by Jesus Christ, and hath given to us the ministry of reconciliation; To wit, that God was in Christ, reconciling the world unto himself, not imputing their trespasses unto them; and hath committed unto us the word of reconciliation. Now then we are ambassadors for Christ, as though God did beseech you by us: we pray you in Christ's stead, be ye reconciled to God. For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him. - 2 Corinthians 5:18-21
It is not that God was through or by Christ reconciling the world but it is that God he was in/to to Christ. A mere man could not do it.