The thing about Jadzia is, she was a great idea for a character, but how do you develop somebody who has lived eight lifetimes already?
I liked what they did with her in Dax, but there's only so many times you can draw from the metaphysical 'who is she really' well. They should have committed to making her a comedy-oriented character.
The writers never knew what to do with the Jadzia character. They should have just written her as an old mentor type of character from the start.
We also got Kes from a race that only lived a short 7 years, but the writers on THAT show didn't know what to do with that character either.
In the case of both Jadzia Dax and Kes, it seems the producers wanted characters that were wise but young, possessing levels of experience far beyond their years. I think Kes was better: the shortened lifespan suggested reaching a level of maturity much sooner without giving her lots of knowledge. She had more social intelligence than other members of the crew, particularly Paris and Kim. Jadzia's level of confidence was not only difficult to believe, it was also difficult to portray. Terry Farrell admits that she needed Avery Brooks help because she could not portray the level of gravitas the part required.
For what it's worth, I think the writers did a better job with Ezri Dax than Jadzia. The kinds of episodes that Ezri got would have been great in the first season. However, the pacing and structure of the last season didn't allow for such introductory explorations of character. Nonetheless, the show needed another female character, and unless they intended to elevate a recurring character to the regular cast/crew (Cassidy Yates? Leeta?), they would need to write a new character, whose presence would be awkward in comparison with the rest.