Well the fact that Kes left isn't what made Voyager better. It's that Braga started to take over, and part of Braga's strengths (yes he actually does have some) is that he made Voyager feel like it was in different part of the galaxy. He was a much more visually driven writer (the show actually felt a little more dangerous, a little more
And more to the point he basically ran (with some suprervision) the staff for seasons 4 through 6 which was the most stable period the show had.
When Voyager started Taylor and Piller worked fairly well together (Berman to settle any disagreements), but then Piller really withdrew to start up Legend. This left Taylor fully in charge of the writing staff, and also took away one of the strengths of the writing staff.
As she took Voyager more towards what types of stories she wanted and got used to being really the sole voice (outside of Berman's occasionally input), Legend failed and Piller returned. Piller had learned from his failure in Legend that Trek's storytelling had fallen behind the times (as its style was very much the same from TNG, and drama's overall were changing in style and tone, while Trek didn't.) Piller pushed for arc based storytelling, of which Taylor was resistant as she felt putting arc material into an episode weakened the primary story. And and both were correct. Storytelling was changing on tv, and Trek wasn't keeping up at all. But its also true that a strong single episode can be weakened by being included in an arc.
While they weren't unfriendly Piller and Taylor's vision of the show no longer matched.
But based on story's and development I would say Piller was getting his way. But then Piller decided to leave Trek and start work again on his own show.
Taylor rewrote the final work of Piller. She then regained basic sole control of Voyager third season (minus of course the 4 hold overs). And it took a while for the writing of Voyage to become consistent (we actually see a strong end to the season with a run of 5 or so episodes).
As for the introduction of Seven an early idea of Braga towards the end of the 3rd season when it was known he would be taking over running the writing staff (with Taylor around basically just to watch over him). There is no question that Braga and the writers started focusing on characters that worked for them. That didn't include Chakotay, Kim or Kes. Now no offense to the actors, but it was clear fairly early in the series run that the writers really didn't find great hooks for some of the primary characters (hardly something new to Trek).
Braga loved seven because she was conflict. It was a serious mistake on the part of Piller, Taylor, Berman and or the studio to basically have the Maquis and Starfleet crew (with a very small number of episodes as exceptions) suddenly become one big happy family.
When we actually saw some tension and serious disagreements between the crews in helped the show, but it was so rare. With Seven it happened far more often.
Now I do think they had about 2 episodes to many devoted to Seven each season, but that extra conflict was a godsend to the show. And no matter how much I liked Kes or the actress that was something she didn't bring to the table. Her's with the exception of Neelix represented the characters that were the easiest to remove from the show.
But I do wish that they could have kept her, even if they downgraded her to a reoccurring special guest star. To use when she was needed.