The first consideration needs to be, ‘What IS a perfect sacrifice?’ That is, from God’s point of view.
The second consideration needs to be, ‘Why must Jesus be human to be a perfect sacrifice?’
The third consideration needs to be, ‘Why must Jesus also be God to be a perfect sacrifice?’
1 – What IS a perfect sacrifice? God provides the answer in the Bible, first, in a negative sense:
“For it is impossible for blood of bulls and of goats to take away sins.” Those animal sacrifices in the ancient nation of Israel were but a reminder of their sin, and the need to approach God carefully, his way, with due consideration for their sins to be symbolically taken up and away, in God’s sight. The previous verses explain this:
“For the law having a shadow of the coming good things – not the very image of the matters, every year, by the same sacrifices that they offer continually, is never able to make perfect those coming near.” The point is made that had animal sacrifices been perfect sacrifices, there would have been no need to keep doing more and more had the guilty had their consciences purified by one perfect sacrifice. No, animal sacrifices only served as “a remembrance of sins every year.”
Then, in a positive sense, that same text explains further that the sacrifice of the body of Jesus Christ only needed to happen once, because that perfect human body was prepared by God for him to offer back to God, that the saved have: “been sanctified through the offering of the body of Jesus Christ once… for by the one offering he hath perfected to the end those sanctified.” (Hebrews 10:1-25 YLT)
The only perfect sacrifice there has ever been was that of the body of Christ Jesus and – it being the only perfect sacrifice ever, no more sacrifices were required.
2 – Why must Jesus be human to be a perfect sacrifice? Again, God’s word In Hebrews (chapter 9 now) states that “…with blood almost all things are purified according to the law, and apart from blood-shedding forgiveness does not come… nor that he may many times offer himself… so also Christ, once having been offered to bear the sins of many…”
As blood represents life, which is God-given, it should always be viewed as sacred and must never be eaten or drunk but returned to the earth – Leviticus 17:11 & Deuteronomy 12:23. That is why biblical sacrifices to God required a living soul with blood in the veins, to have that blood shed. Hence, the only perfect sacrifice had to be a perfect body with blood in the veins, sacrificed to God.
Therefore, Jesus had to have a perfect human body with blood in his veins. That is what God prepared for him. Jesus could not be a mere apparition of humanity. He had to be fully human to fully represent all humanity.
3 – Why must Jesus be God to be a perfect sacrifice? God is Spirit. God is a divine Being and by nature, divinity is what God is. That is the nature of his Being. A human being is, by nature, human. That is what a human is. That is the nature of humanity. You cannot become what you are not. God has always been God, for that is the very nature of his Being; that is what he is. Yet the one who made everything that was made (the Word of God, who was with God in the beginning, and who is God – John 1:1-3) made man in his image. Therefore, the Word, who became flesh as the man, Jesus, was not becoming what he was not. He was appearing in the flesh, human flesh, which he had made in the beginning as the first man, Adam. Spirit has no blood. Therefore, the Word became flesh [and blood] “and dwelt among us, and we beheld his glory, that of the only-begotten of the Father, full of grace and truth” (John 1:14).
The text in John 1 states that the Word, who became the man, Jesus, was God. You ask “Why?” Because all humans stood condemned under God’s law as law-breakers. The first Adam brought about that collapse into sin which none of us can extricate ourselves from. Now, if the man, Jesus, had not been God incarnate, but born as are all humans from the stock of Adam, he would have been in the same plight as ourselves. He would have required another to cover his own sin. He could never have been sinless. No creature (i.e. a created being, as are all human beings, as are all angelic beings) could have the magnitude of deity needed to deal with the immensity of sin, death, and the devil.
This is where the love of God becomes staggeringly awesome. God knew that nothing we could do would save us from the punishment due for our many sins, so the Son of God agreed to become a flesh and blood human, to be the one, perfect sacrifice, where God would pour out on him the punishment due for all sinners who were to be reconciled to himself. Christ became sin as he died (for “accursed is every one hung on a tree” – Deuteronomy 21:23), though he was without sin! And, because he died sinless, death could not hold him. God raised his Son from the dead as proof that he truly was, and is, the Son of God (which is an ascription of deity). See Romans 1:1-4.
As the question itself raises the vital point of blood being shed to deal with sin, I have agreed with that, then gone on to show that sinlessness can never be achieved by a created human being, so for a once-for-all-time perfect sacrifice of blood, a sinless human was required who was uncreated. That only ever could be the one who created humanity in his image - the one who made everything that was made, hence (logically) not having been made (created) himself - God incarnate.