Why was Michael Dorn in Star Trek DS9 and not someone else from TNG?

Here is an interview with Michael Dorn on TrekNews.

He opens with the line "It was just a backstory." Which maybe means it wasn't intended to be long term.

Can you talk about some of the factors that led to you joining the cast at that time?

Dorn: It was just a backstory. We [Star Trek: The Next Generation] ended in ’94 and we did a movie real fast and were kind of guaranteed we were going to do another movie after that. So my life went on, back into the acting world with auditioning and things. Then in ’95, just a short year later I was doing a video game in Baltimore called “Mission Critical” and I was in the hotel after a couple days and I got a call from Rick Berman. Rick and I are close, we talk and he said “Michael I want to ask you something,” he said “What would you think about coming back and reprising your character on ‘Deep Space [Nine]’?” I was surpassed and I was sort of like “OK” you know? “It sounds interesting.” It shouldn’t be a surprise, things strike me differently at times and it shouldn’t have been a shock, but that’s what got the ball rolling. From there it went to our representatives. While that was being done I had a meeting with Rick [Berman], Ira Behr and Ron Moore, just to say “look this is going on, but I want you guys to understand that I love the character and I’m very tenacious about holding onto what makes Worf who he is and the one thing I don’t want is to be standing around in the background, just to sort of give the show a boost and I don’t really do anything. That would be terrible. I really want to have episodes that concentrate on my character and I want him to open up as a character.” They assured me, they said “Yes, that’s our plan,”. After some back and forth between our representatives, that’s what happened. The two things that I–and haven’t really told Rick this, but I say it sometimes–the first thing is that I want the character to open up, but on a personal level, it was the idea that it was a challenge and I really love challenges. The challenge was basically they were coming to me saying we want to reprise your character because we want to inject some other stuff into Deep Space Nine that will help with the ratings basically.

Season 4 marks the beginning of the Klingon invasion of Cardassia, leading up to the alliance between Cardassia and the Dominion. These may be some of the elements he mentions as "inject some other stuff into Deep Space Nine" and they logically thought, well if we are going to bring in all these Klingons, we might as well bring in the most famous one.