One explanation that occurred to me is that דווקא because of the very strong connection (for example) between God and His mercy, the statement “God is merciful” has no meaning. Let us first say that with an ordinary human being, if he changes from being merciful to being cruel, he still remains the same person, but that probably cannot be said of God, since His mercy is ingrained in Him by virtue of His being God and cannot be otherwise. But even here there is still no real problem, and it seems to me one can say even more than that—and in this perhaps answer the question of why it does not make sense to speak of Him in essential attributes (and also what value there is in the doctrine of negative attributes): in fact, one cannot relate to God’s mercy the way we relate to an essential attribute, because even assigning God’s mercy to an attribute that is essential to Him would lead me to a mistaken conception of Him.
And by way of analogy, one can say that one of a human being’s essential attributes is that he is a speaking being, but even if we remove his being a speaking being, we can still say of him that he is a human being—just a deficient one. That is not the case with God: if you remove His mercy, it is not God at all. Unlike a human being or any other entity, one cannot say that God is characterized by mercy and patience, and an indication of the failure in that can be seen in the following thought experiment: if I imagine to myself God, except that now He is only patient and not merciful, I would be picturing in my mind “a deficient God,” like what we called a deficient human being. And that is an oxymoron. That is, God cannot be conceived without His being merciful, for then we would not be speaking of God at all. In fact, it seems, to use Kant’s terminology, that His being merciful is not synthetic for Him but analytic. And an attribute, even an essential one, seems to me semantically synthetic (though perhaps there are attributes that are analytic to a concept, but one would need to think about whether those are what we ordinarily call attributes, because in some sense we expect attributes to add information about the thing).

What you are describing is entirely positive attributes, except that you claim they are not attributes but part of the definition of His essence. From Maimonides’ standpoint that is even worse. You said something positive about Him. What difference does it make whether that something is not an attribute but the definition of His essence?

Why is that worse from Maimonides’ standpoint? Does Maimonides say that nothing positive at all can be said about Him? Besides, I was not necessarily speaking specifically about Maimonides. The Kuzari, Duties of the Heart, Beliefs and Opinions, and others also speak specifically about attributes. But thinking about it further, what you yourself said actually explains my claim. In truth I did not say anything positive about Him, because in fact I said something completely devoid of meaning. I did not really make His essence known, since I used an attribute in order to do so. To clarify more what I was suggesting—why such things cannot really be said—I want to argue that one cannot understand what I mean (that is, it lacks meaning) when I say that the quality of mercy is part of the definition of His essence, because it is after all only a quality, and a quality cannot explain to me the content of the thing itself—that is, His essence—but only characterize the content of the thing (the entity itself is not “made of” qualities). Therefore, even if the quality is necessary to His essence, it cannot serve as an explanation of His essence, and so to say of Him that He possesses the quality of mercy—when if He lacked the quality of mercy we would no longer be speaking of God at all—is a sentence devoid of sense syntactically, because this is not an attribute in its semantic sense.
Just to explain this line of thought a bit more, Rabbi HaNazir brings in his book The Voice of Prophecy, “The Supreme Name That Is Heard,” section 7: “And in the end he says (about Rabbi Yehuda Halevi in the Kuzari), ‘And we call Him wise of heart, because He is the essence of wisdom and wisdom is not an attribute of Him.’”
And also in note 22 there: “David Kaufmann, ibid., p. 152, note 91. On the strange matter that departs from the fundamental principle, explaining the Divine as wise of heart, we will have to deal with this. And he deals with it later there, pp. 163–164. And in the notes there he brings the words of Rabbi Moses ibn Ezra, in Mikveh Tziyon, vol. 2, p. 134: The philosopher Empedocles said, when it is said of the Creator that He knows, this means that He is knowledge itself, not that knowledge is attributed to Him.”
In any case, all this is only a suggestion for why the philosophers of old held that He cannot be described in essential attributes (I do not know whether they held that nothing positive whatsoever can be said about Him). I would be happy to know your opinion.

I did not understand a thing. Bottom line, you said something positive about Him. Are you suggesting that this statement says nothing? Then what did you gain?

I am saying that the philosophers in the past claimed that saying of Him that He is merciful is similar to saying of Him that He is wise of heart, as brought in the Kuzari: “And we call Him wise of heart, because He is the essence of wisdom and wisdom is not an attribute of Him.” Therefore it is not a positive attribute. And as for your question, I also do not think they meant that by this we have said something positive about Him; rather, only by analogy do we call Him wise or merciful, but that does not mean that He is wise or merciful in the simple sense of the word (and therefore He is only not foolish and not cruel).
To be honest, I also do not fully understand this distinction, but it seems to me that this is the debate that was going on in their minds.
Of course, it may be that I am mistaken and they meant something else.