Well, cosmic horror is defined as coming up against the unknowable and the incomprehensible. If you "learn" things about the horrors, they are things that are incompatible with sanity, by definition. So, yeah, the core tenet of cosmic horror is that you can't stay sane in the face of the horror. The knock on to this is that you just can't beat up the horrors. Some, sure, but these are minor plot movers or serve to damage the sanity anyway.
You port this into D&D and you run into problems straight off. Firstly, D&D character's mental states are inviolable normally. They can be temporarily affected by a spell or condition, but even then the actual thinking of the PC is under the sole control of the player. This is a core tenet of D&D -- the player controls the PC's thinking and feeling. So, the effects of going against the incomprehensible is already running afoul of D&Disms. The second thing is that D&D characters are super charged with combat effectiveness, and the D&D ruleset requires monsters be built under the combat system. Not doing so tosses the majority of the ruleset.
All this goes to say that the actual genre of Cosmic Horror is largely incompatible with the D&D ruleset. You are not changing genres, in other words, with a hack that adds some mythos but keeps 5e recognizably intact. Instead, you're playing the D&D genre and adding in some Cosmic Horror spice. That you didn't go with any sanity loss is a great indication, here, not of your understanding of the Cosmic Horror genre (if so, then you misunderstand it's core components) but rather that you've chosen to prioritize the D&D genre over Cosmic Horror. You've chosen to play D&D with a few tentacle horrors and a few bits and pieces of scenery color. And that's great. But it's still 5e doing 5e with a few bits of extra color, it's not a change in genre to Cosmic Horror. You aren't doing Cosmic Horror, in other words, you've just borrowed some scenery -- the play is still D&D.
This is the issue, though. For people that actually shift to different genres, this is apparent. The change is not a matter of some scenery changes and a few tidbits tossed out, it is a fundamental shift in what's important and how things are expected to work. Genre logic changes between genres. So, when it's suggested that someone wants to do genre A, these assume that genre A is the actual goal, and recognize how hard it is to move to genre A with a game firmly rooted in genre D&D. So they recommend a game that does genre A well. But, the question is often misphrased or misunderstood by the asker -- they don't actually want genre A, they want genre D&D with some genre A set dressings. So, the recommendation for a different game seems insulting because the unstated ask is that genre D&D still be the primary genre, and how can you get that if you're not playing D&D?!