Question: If the elect angels are sinless, why couldn't an angel have been sacrificed instead of Jesus? Is it because only God could be in human form and not sin?
Answer: Your proposed answer is a good one. Let me sort a few things out though, because some of the terms may mean different things to different people. But first, let me state emphatically that no angel, elect or otherwise, could ever redeem a human being. Why not? Because we are different types of creatures.
Sure, we share some characteristics with angels, like being creatures, being sentient, and possessing free will, but we are fleshly beings whereas they are spirit beings. As such, they have no blood to shed—and blood is an absolute requirement for atonement (Heb. 9:22). Furthermore, since angels are not human by type, they are not (nor could they ever morph in such a way as to become) our kin, and redemption requires a kinship relationship between the redeemed and the redeemer. Indeed, the entire book of Ruth develops this theme. Lastly, only we humans are created in the image and likeness of God (Gen. 1:26). This is said nowhere of angels. We humans were purposefully created for a unique relationship to God. We are designed to be sons (Gal. 4:6), whereas the angels are servants (Heb. 1:14). As such, no angel meets the qualifications for a redeemer.
God requires three things of a redeemer: kinship, the ability to pay and the willingness to pay, and Jesus is singularly qualified as mutually meeting these requirements (Acts 4:12). You have correctly noted that Jesus took on human form, all the while remaining sinless. In so doing he fulfilled the first requirement—that of kinship.
“And the Word became flesh and dwelt among us, and we have seen his glory, glory as of the only Son from the Father, full of grace and truth.” (John 1:14, ESV)
“Great indeed, we confess, is the mystery of godliness: [Jesus] was manifested in the flesh, vindicated by the Spirit, seen by angels, proclaimed among the nations, believed on in the world, taken up in glory."
(1 Timothy 3:16, ESV)
Jesus’ ability to pay the price for sin is a function of his own sinlessness. He alone was able to pay the price because he alone possesses the coin-of-the-realm, holiness. So, the transaction came down to blood for blood, his for ours, the holy for the profane.
“For we do not have a high priest who is unable to sympathize with our weaknesses, but one who in every respect has been tempted as we are, yet without sin.” (Hebrews 4:15, ESV)
“You were bought with a price; do not become bondservants of men.” (1 Corinthians 7:23, ESV)
“knowing that you were ransomed from the futile ways inherited from your forefathers, not with perishable things such as silver or gold, but with the precious blood of Christ, like that of a lamb without blemish or spot.” (1 Peter 1:18–19, ESV)
His willingness to bear our sins is evidenced by his foreknowledge, his joy and his obedience.
“And he began to teach them that the Son of Man must suffer many things and be rejected by the elders and the chief priests and the scribes and be killed, and after three days rise again.” (Mark 8:31, ESV)
“looking to Jesus, the founder and perfecter of our faith, who for the joy that was set before him endured the cross, despising the shame, and is seated at the right hand of the throne of God.” (Hebrews 12:2, ESV)
“He himself bore our sins in his body on the tree, that we might die to sin and live to righteousness. By his wounds you have been healed.” (1 Peter 2:24, ESV)
As you can see, Jesus is mutually unique in the three requirements. He alone is human, able and willing—all at the same time! Now, consider your alternatives. If I decided to pay the price for your sins, only two qualifications would be met. I am human (thereby related to you), and I would be willing. However, since I too am a sinner, I would not be able to pay for your sin, because my personal sin binds me in a crippling debt, the recovery from which is hopeless. Now let’s say that an elect angel were to try the same thing. He would also meet two requirements. He would be willing, and he would be able (via his sinlessness), but he would be categorically disqualified as a redeemer because he was not related to you. You are a human. You need another human to redeem you. The angels’ heavenly viewpoint gives them no advantage in redemption. In fact, there are indications that they did not even know the details (1 Pet. 1:12).
Please note that angels frequently take on human form in the Bible, but this is for purposes of communication. They appeared human. They did not become human. It is important to understand that these appearances are not the equivalent of Jesus taking on humanity. He was born of a woman and grew into full adulthood like all of us. Angels do not do that. They appear as fully adult, and they pop in and out of the physical world.
As a closing thought, try not to add too much weight to phrases like “elect angels.” First, that phrase only appears once. Yes, it’s in the Bible…but thinly so, with no other showings for comparison. Secondly, Paul uses this phrase to ramp-up to his main thought, so you cannot consider this a teaching on angels per se. Thirdly, the Bible is pretty clear that there are two categories of angels: the fallen and the unfallen. Whether or not unfallen mean sinless is up for debate. But Jesus’ sinlessness is not up for debate. He has a holy nature. He cannot sin. The angels are not intrinsically holy. This is evidenced by their fallen ones.
Also, when you hear the term elect, try not to go into theology mode. It just means the chosen ones, which is common and broadly applicable. For instance, Jesus was not elected to sinlessness. That is part of his nature. Yet he is referred to as “elect” (Luke 9:35, 1 Pet. 2:4). So also are God’s Old Testament chosen, Israel (Isa. 45:4) and his New Testament chosen, the Church (Eph. 1:4). My point is that the word elect is more common than many theologians would like you to think. This is why I advise keeping the phrase elect angels on the back burner while keeping solid doctrines like Redemption on the front.
I pray that all this helped.