This is a great question which perfectly illustrates an ongoing discussion and also a schism between two schools of philosophy. Very broadly speaking, there is on one side analytical philosophy and on the other continental philosophy. And one of the point of contention is the relation with the history of philosophy.
Analytical philosophy likes to think (again, broadly speaking) that history of philosophy means reading old books and confronting what is written with our own thoughts. On the contrary, Continental philosophy emphasizes on the fact that we, now, do not read the same book as people did four hundred (or more) years ago. And this is not because of the book, but because of us.
On a superficial degree, this is simply because the meaning of the terms can change. Obviously, this is not what analytic philosophers may miss. But more deeply, as the terms, the concepts with which we think (and so with which we read) also have their own history and their own birthdate. Those concepts may seem natural to us, but they are mostly inherited and they condition the way we understand things.
Two prime examples are the concepts of existentia1 and voluntas2 (willingness). And another great example is the invention of the consciousness as in self-consciousness. While the term "conscious" (or "conscience" in French), from the latin conscius, was used way before Descartes, it only acquired its philosophical meaning in the 17th century! It is sometimes attributed precisely to Descartes who writes in Principia Philosophiae, I, IX, AT VIII-1, 730
But if I understand from sensation or the conscience of seeing or walking...
(Sed si intelligam de ipso sensu sive conscientia videndi aut ambulandi…)
But it is also sometimes attributed to Locke in his An Essay Concerning Human Understanding. He write in II.i.19 : "Consciousness is the perception of what passes in a Man’s own Mind". If you can read French, this book chapter from Étienne Balibar is a great attempt at clearing this. It is based on the translation of Locke's essay in French done in 1700 by Pierre Coste and on choices of translation which may now appear (now that this concepts of consciousness is ubiquitous) as peculiar (while still sensible). This is also a great example of methodology of continental philosophy.
And now to answer your question (but I think the answer is already getting clear), as both Locke's essay and Descartes's Principia are posterior to the meditations, Descartes simply didn't have yet on hand the concept of consciousness which he could have used to conceptualize his findings as you suggest. It's the other way around—he was precisely working toward the conceptualization of this concept through his findings!
- Root of the word existence, the Latin word existentia is built as a substantivation of the verbe exsistere (ex-sistere): to make something stand, to place something (sistere) out of something (ex-). Marius Victorinus coined the term in the IVth century in the theological context of the trinity: the father and the son are one, but at the same time the father is not the son and the son is not the father. How can those two affirmations be conciliated? The answer of Marius Victorinus is the following. The son
is ex-istantia of the father: he is the manifestation of the father out of the father; that is, he is the generation by the father in which the father ex-ist. As the apparition of the father, the son and the father are one; but the son is not the father and the father is not the son. See V. Carraud, "l’invention de l’existence", Quaestio, 2003, pp. 3:-26.
- Voluntas gives in French volonté (willingness). One theory is that it was introduced by the theologian Augustine in his De libero arbitrio. Augustine, throughout his difficult life, was frequently drawn to the following question: what is the origin of sin in a world created by god, which itself is good? For him, if there is sin, as it can’t originate from god, it must come from man. And here comes into play the voluntas, for which there was no Greek equivalent: for the human being to act wrongly, he must be given the possibility of
doing either the right or the wrong thing; in other word he must be given free will, and with it the muscle of well-doing: the voluntas. Note that this attribution to Augustine is sometimes discussed, see for example Michael Frede. A Free Will: Origins of the Notion in Ancient Thought pp. 153-174.