And the same goes for arguing how TNG or the Picard series can rely on the past while scoffing at the same arguments for Discovery. Picard is the main character, so obviously he should catch up with everyone else he worked with 20 years ago on their favorite show... but a main character being involved with the family that raised her her whole life is unbelievable fanwank. Let's promote O'Brien to the main cast under the command of the guy whose wife was killed by Picard, also let's spend 4 seasons expanding on Worf's backstory, but using Pike (who appeared in one episode), expanding on the Sarek family and making him a recurring character, oh dear god the oversaturation.
It's obvious that some people just aren't interested in TOS, didn't want a prequel set in that era, and don't care for Burnham as a character, which is all fine. But for some reason they feel the need to perform these mental gymnastics to try to convince themselves and others that it's all wrong, instead of simply admitting they have subjective preferences.
DS9 was pretty obviously the most fanwanky of the Trek series overall. In addition to what you mentioned, remember that Kira was originally supposed to be Ro. They made attempts to bring back many TNG characters - some of which failed (Q, the Duras sisters, Tom Riker) and some of which became recurring (Gowron, Lwaxana). Most fundamentally, everything in the show - minus the Prophets, the wormhole, and the Dominion - was just deepening existing Trek lore, from the Cardassian occupation of Bejor, to the Maquis, to the Ferengi.
The interesting thing is out of the Berman Trek shows, DS9 was actually the most distinctive and least like TNG in spite of this, because they changed the setting, and the format in which they told stories. In contrast, VOY and early ENT tried to escape elsewhere in space and time respectively, but given they had the same underlying framework as TNG and were telling the same kind of stories, it didn't seem distinctive even when they avoided bringing back familiar faces and races.
Still, I don't think the relationship of DS9 to TNG is analogous to the relationship between DIS and TOS. I mean, past the pilot, did Sisko ever mention Picard again? And even after Worf was brought onto the show, I don't remember him and O'Brien really talking much about the good old days on the Enterprise. The little callbacks we did get were meant as nice Easter eggs to the viewers, but there was never once the feeling that the TNG characters were overshadowing those on DS9. Which is unfortunately what I'm getting fro Burnham this season - that she mainly exists to be the exposition-fairy for Spock, who has yet to be seen. I prefer Season 2 overall to Season 1 so far, but I preferred Burnham's role in the first season, because at least she seemed to be integral to the narrative as something other than a sibling to a guy far more famous than she is.
