Your analysis is faulty in that DS9 bled viewers/ratings from it's very first episode, at about the same rate as every other Star Trek series after Star Trek the Next Generation.
There's also the aspect that as Internet viewing and other forms of media viewing options and diversions began to become available for people, syndicated and network viewing overall began to decline as well across the board. The only Star Trek series that gained viewers after it's pilot episode aired was Star Trek the Next Generation.
Every other Star Trek series from DS9 to Enterprise bled viewers at about the same rate. Remember that the reasons that the Starship USS Defiant was added in season 3, and Michael Dorn as Lieutenant Worf was added in season 4, and making the Klingons the Federation's mortal enemy again in season 5 was all to try and stop the viewership bleed, and see if they could gain back some viewers overall. In the end none of these strategies worked as they had hoped.
Yes viewership numbers were high enough to continue producing DS9 episodes (even though some stations bought at an increase in the licensing fee for season 7, and as a result some of these syndicated stations stopped airing new DS9 episodes for a few weeks at the start of that season while they negotiated with Paramount); again the fact is that every series after TNG bled a lot of viewers after the pilot episode.
ENT probably would have made it to 7 Seasons as well if there hadn't been an upper management change when Les Moonves was promoted to CEO of CBS in 2003, and oversaw the merger of the UPN and the CW. (and remember that Viacom which owned Paramount at the time, purchased CBS in 1999.)
If Les Moonves had been in charge at Paramount at the time of DS9, it probably would have been canceled after it's 4th season and it had made the requisite 100 episodes required for striped indication back in the day. (And in fact that was the only reason Enterprise got a fourth season, as that gave it 98 episodes which was close enough to the magic 100 episode number.)
If he had been directly in charge at that time, Voyager and Enterprise probably never would have happened.