Badiou published only one letter (translated here) from that correspondence. Deleuze was very exacting, perhaps even tyrannical with his texts, refusing interviews, repeating some formulations of key concepts almost word for word for decades. It is regrettable regret that he forbade publication of the letters. The only effect that this has had is that probably they have circulated privately, and that an élite few have had access to the correspondence.
Badiou published one of his own letters, and doesn’t quote Deleuze in it. So he respected Deleuze’s wishes rather well, beyond what Deleuze had a right to demand. Deleuze was willing to engage a dialogue with Badiou, but unwilling to follow through to the end. It is very difficult to evaluate this gesture of ending the dialogue. However, we must also say that the same applies to his opening the dialogue with Badiou in the first place.
According to Lyotard recent French philosophy has had in common an acute awareness of, and sensibility to, the incommensurabilities that traverse and fissure the plural reality that underlies our illusions of unity and of homogeneity. Lyotard specifically includes Deleuze in this configuration of thinkers, declaring that Deleuze by way of his reflection on “the effect of sense by nomadic encounter…put the accent on incommensurabilities” (from “Appendice svelte à la question postmoderne” in TOMBEAU DE L’INTELLECTUEL, page 85, my translation).
Yet Deleuze himself has always practiced what Badiou calls “convergent” dialogue. He required a form of friendship that was quite selective. This insistence on (perceptual, affective, and conceptual) convergence and friendship valorises consensus and introduces a form of meta-commensurability in an enunciation that talks of, and nourishes itself from, incommensurabilities. With Badiou the dialogue was “divergent”, and thus closer to real life for most people. We cannot all insist aristocratically on a high degree of convergence with our dialogical partners, and the divergent dialogue is the more democratic.
On this point Badiou was doing his job, that of proposing to go even further in the practice of incommensurabilities, and of detecting unitarian prejudices continuing even within the practice of one of the most consummate ontological pluralists. These unitarian prejudices, and the pragmatic contradiction between the convergent style and the divergent message, have neutralisedsed Deleuze’s followers, often condemning them to a sterile repetition of his formulations rather than a real fundamental critical discussion.
Given that Deleuze himself did not accept dialogic reformulation of his ideas in radically different terms the result has been the propagation of a dithyrambic evocation of concepts under the guise of what one may call a “Deleuzian doggerel”.
On the ethical point of whether Badiou “should” have published his letter to Deleuze, it is difficult to avoid a sense of hagiographic distortion here, in which “saint” Deleuze is seen to be betrayed by the “demonic” Badiou. In fact, Deleuze quoted quite freely from Kafka’s posthumously published writings despite Kafka having ordered that they be burned. There is a double standard here.
Finally, I think that Deleuze was perhaps badly advised by his entourage, and that the non-publication of his correspondence with Badiou is a loss for philosophy.