The Logos became incarnate as a human being, to save us from our sins. There would have been no similar point to his becoming incarnate as a cat, an oak or a photon? But could he have done so, if he had a purpose to?
Suppose we say "no" to at least one of the three options (cat, oak or photon). Why would we? Assuming we accept that the Logos could have become incarnate as a human being, we would have to suppose some relevant difference between humans and cats, oaks or photons. What the difference is will depend where one draws the possibility-of-incarnation line. If one thinks that God could have become a cat but not an oak, that's presumably because one thinks that sentience is crucial to the possibility of incarnation. And one will presumably then deny that God could have become a photon. If one thinks God could have become a human but not a cat, then presumably one thinks sapience (and I won't worry about the details of what the consists in, say agency or abstract thought) is crucial.
But we human beings don't always exhibit sentience, much less sapience. We don't exhibit sentience for the first weeks of life after conception, and we don't exhibit sapience until at least around one year after birth. Moreover, when unconscious we do not exhibit sentience and need not exhibit sapience (though, maybe, sapience doesn't always require consciousness). In becoming one of us, the Logos would have become a being that wasn't always sentient or sapient. So if one thinks that sentience or sapience is crucial for incarnation, and yet one accepts that the Logos could become a being like we who does not always have sentience or sapience, one has to say that it is something like the potential for sentience or sapience (depending on which view we are considering) that is a necessary precondition for incarnation or that it is sometimes having sentience or sapience that is necessary.
Consider first the "sometimes" view. This presumably requires that the incarnation cannot precede the developmental attainment of sentience or sapience (for the incarnation does so precede, we could imagine it terminating, with the destruction of the finite nature, before that attainment). If sapience is the relevant condition, then we get the view that barring miraculous precociousness, God cannot be incarnate as a newborn, which at least to us Christians will be absurd. If sentience is necessary, then we get the view that, again barring miraculous precociousness, the incarnation couldn't have happened simultaneously with conception. (Interestingly, Aquinas actually goes for miraculous precociousness here—his view that we don't come into existence at conception but a significant amount of time thereafter forced him into holding that Jesus came into existence fully formed in Mary's womb.)
Still, the "sometimes" view just seems implausible. Why would the incarnation require initial exercise of sentience or sapience without the need for exercise of sentience or sapience thereafter?
Now consider the potentiality view. This, too, does not seem all that plausible to me. Presumably the pull of saying that God couldn't become a cat or an oak or a photon is that these beings are so very unlike God. But potentiality is very much unlike God's perfect actuality, too. In the end, I think that once one reflects on the fact that human beings often exhibit neither sentience nor sapience, the pull to thinking the Logos couldn't have become a cat or an oak weakens.
How about a photon? There the relevant difference would be something like life. But again it seems hard to see why life is a necessary condition for an incarnation. There are, plausibly, infinitely many attributes as significant as life that God has and that human beings lack. The gaps between the photon and the oak, the oak and the cat, and the cat and the human are infinitely less than the gap between humans and God, a gap that God can bridge, we have assumed.
The above arguments are not very strong. But I think they do give one a presumption in favor of the view that if God can become incarnate as a human, he can become incarnate as any kind of being.