It’s one of the enduring puzzles of scholarly interest in Calvin’s Institutes that he can’t seem to make up his mind as to whether the incarnation was necessary or not for human beings to enjoy fellowship with God.
Calvin wrestles with this at the start of Book II, chapter xii. On the one hand, he denies the absolute necessity of the incarnation. God wasn’t compelled to send His Son (no-one twisted His arm to make Him do it). This safeguards grace. Things could have turned out differently had God willed to unite His divinity and our nature some other way.
Any necessity it does have derives from His free and gracious choice to redeem us so that we unholy sinners could dwell with God and He with us.
On the other hand, Calvin maintains that ‘Had man remained free from all taint, he was of too humble a condition to penetrate to God without a Mediator’. That is, it’s impossible for human beings to enjoy fellowship with God without a Mediator. And that Mediator had to be near to us — knowing our human situation from the inside, and ultimately draining to the dregs our plight and God’s judgement on it.
Putting the pieces together, I would suggest that the necessity of the incarnation is not a matter of abstract propositional or philosophical necessity but rather it’s a matter of narrative necessity. As Richard Hays puts it (The Faith of Jesus Christ, p 195):
[T]he coherence of events in a narrative is characterized by fitness rather than by logical necessity … If we ask why the events of a particular story are ordered as they are and not in some other way, the answer can only be “because that is the way it happened” or “because that is how the story is told”.
Calvin, like all good theologians, does his theology after the fact and won’t relinquish either God’s grace or the fact that if there’d been any other way for God to secure our redemption than by giving up His own Son surely He would have pursued it!