Well, in fairness, I believe the guy that got caught posting classified docs in a small private discord server would appreciate privacy, even if I myself and a lot of people almost exclusively use public servers and would prefer if they were even less private so internet search would work.
His friends passed the documents along to their friends, and they eventually got the attention of the New York Times. At that point tracing the documents back to him would probably have happened regardless of whether he used IRC or anything else.
Do you have any evidence that him using a centralized platform like Discord played a role in him getting caught?
The Buffalo shooter organized on a public Discord and unfortunately that had no effect in preventing him. But, this is getting back to my initial point, you are using Discord because you are hoping for private communication then you are using the wrong product.
Hypothetically speaking if instead of using Discord normally and using his real info for billing Discord only accepted Monero and was only accessible via Tor it would be harder to identify him.
But that's not really my point, just picking a random famous example of someone who would want Discord to be private.