That's the thing about writing. the DS9 crew gets along just fine without a counselor for 6 years. Then, Ezri shows up and Sisko goes nuts. They invented "counselor stuff" for Ezri to do because her position couldn't be worked into the show without it.
They most certainly were not fine psychologically until Ezri showed up. They were probably the most psychologically screwed up crew of any Star Trek series, especially compared to TNG, where there were far fewer conflicts between the crew because they all got along so well most of the time. And I almost laughed at the line, "Ezri shows up and Sisko goes nuts". How many times did we see Sisko go crazy in the first six seasons? Too many times to count! That's why many of us (including myself) have criticized Brooks' performance for being too over-the-top sometimes - it's not just the actor's fault, because there were just so many scenes where he had to act like he was having a temper tantrum or a nervous breakdown and that's hard for any actor to pull off!
To brighten up the Ezri talk on this page, I'd just like to state that I'm watching season 7 for the first time and I consistently find her to be the best part of every episode (which is similar to how I felt about Jadzia, especially in the early seasons). I find watching what she says or does in reaction to the situations in the episodes makes them a lot more interesting, which again is something I felt about Jadzia, so it's safe to say that I feel the transition from one Dax to another on the show has been handled about as well as it possibly could be.