It would be nice if He told us He did it, if He had done it.
He didn't tell us because He didn't do it: the antidote to the basis of the IC-potuit, decuit, ergo fecit.
So God told us about everything He did?
Everything that non-belief thereof would lead to hell fire through a "shipwreck of of [our] Faith," yes.
And that is the big problem with the IC: as St. John of Damascus warns from the start of "The Orthodox Faith" as a first principle:
Chapter 1. That the Deity is incomprehensible, and that we ought not to pry into and meddle with the things which have not been delivered to us by the holyProphets, and Apostles, and Evangelists.http://www.newadvent.org/fathers/33041.htm
No one has seen God at any time; the Only-begotten Son, which is in the bosom of the Father, He has declared Him. The Deity, therefore, is ineffable and incomprehensible. For no one knows the Father, save the Son, nor the Son, save the Father. Matthew 11:27 And the Holy Spirit, too, so knows the things of God as the spirit of the man knows the things that are in him. 1 Corinthians 2:11 Moreover, after the first and blessed nature no one, not of men only, but even of supramundane powers, and the Cherubim, I say, and Seraphim themselves, has ever known God, save he to whom He revealed Himself.
God, however, did not leave us in absolute ignorance. For the knowledge of God's existence has been implanted by Him in all by nature. This creation, too, and its maintenance, and its government, proclaim the majesty of the Divine nature. Wisdom 13:5 Moreover, by the Law and the Prophets in former times and afterwards by His Only-begotten Son, our Lord and God and Saviour Jesus Christ, He disclosed to us the knowledge of Himself as that was possible for us. All things, therefore, that have been delivered to us by Law and Prophets and Apostles and Evangelists we receive, and know, and honour , seeking for nothing beyond these. For God, being good, is the cause of all good, subject neither to envy nor to any passion. For envy is far removed from the Divine nature, which is both passionless and only good. As knowing all things, therefore, and providing for what is profitable for each, He revealed that which it was to our profit to know; but what we were unable to bear He kept secret. With these things let us be satisfied, and let us abide by them, not removing everlasting boundaries, nor overpassing the divine tradition Proverbs 22:28 .
The divine Tradition knows nothing of an "IC." The Vatican's Scholastics tried to get around that with "potuit, decuit, ergo fecit."
Cataphatic theology depends on the revelation of God. Overpassing it Apophatic theology reigns, otherwise theology leads to heresy: splitting hairs when a simple answer is rejected. The IC is not only an ingenious solution in search of a problem, but it is based on an argument ex silentio, making pronouncements where God has said no such thing: it argues on an analogy between Christ and His mother as to her humanity on the relationship between His humanity with His divinity.
Christ and the Father (and the Holy Spirit, but just to keep it simple, like the Gospel does) share the same divine will. Yet Christ says "Your will, not Mine, be done" at Gathsemene. That can only be the human will, which the Father does not share, although in the person of Christ it is united with His (the Father's) will. That will in Gathsemene resembles how the Son, but not the Father or Holy Spirit, suffered in the flesh on the Cross.
Since Christ is the New Adam, He would have everything that Adam had, except sin. But then, Adam didn't have sin until the Fall, although he obviously had the potential.
In the Resurrection, both that potential and its effects are burned away by the fires of Theosis, as none will fall from paradise (contrary, IIRC, to some ideas Origen had on the matter).
In the meantime between the Fall and the Resurrection, is the gnomic will and the ability to sin, i.e. ancestral sin, a necessary part of humanity? Obviously not, as it will not be resurrected, and Christ did not assume it in the incarnation. Why not? Because Christ's divinity cannot sin by its nature. The divine nature cannot suffer by nature either, but He could and did freely choose to unite to humanity, and through the Incarnation the Son (but not the Father nor the Holy Spirit) could and did suffer the effects of sin. But to sin would entail Him to be able and to freely choose to go against His nature, for the Son to use His will against His Father's. Such is impossible, as the Son and the Father share the same will.
The gnomic will and the ability to sin, i.e. ancestral sin, is not a necessary part of the human being, but it is a universal part of the human condition, save one. It is because the Son only had one will (which He shares with the Father) to unite to the human will He took from His mother, or had only one will which was incarnated of the Holy Theotokos, ancestral sin could not be transmitted, as transmission would entail not only the human nature annihilating the divine nature, but something not of the essence of human nature (i.e. sin-otherwise Adam would not be human until the Fall) overcoming the divine essence. For the incarnation to occur with each nature retaining its essence in one person, the gnomic will would have to be burned off like dross in the womb of the Virgin. Only in that way, in the Incarnate Christ with His divine nature and His human nature united without confusion but without seperation, could human free will be maintained and sin defeated.
That is why the Nestorian Christ would not work: the Word would redirect the human will of the man He assumed, but the gnomic will would still be left intact, only losing its freedom by association with the divine Will of the Word. So too why the IC is incorrect: only a hypostaic union of the divine will could eliminate the gnomic will without destroying human free will. Only in the Orthodox understanding of the divine will and the human will in the hypostatically united will of the one person of Christ is the Good News proclaimed.