Television shows have budgetary constraints. They're only given so much money. When the producers decided to introduce a new series regular, they were forced to remove an existing cast member. I really don't think they could afford to pay 10 series regulars. So the decision to fire someone was budgetary more than anything else. As for who the producers chose to cut, that was likely much more political. I'm sure the producers had certain favorite characters that they didn't want to lose. I'm sure the writers also had their favorites. The studio and the network threw in their two cents, as well, I'm sure. The popular rumor is that Garrett Wang was singled out to get the axe. Harry Kim's fate was pretty much sealed when he gets critically injured in "Scorpion, part 1" and he could have very easily died in the season 4 premiere. However, the show and the actor were given a publicity boost when Wang was named one of People Magazine's most beautiful people of the year. I'm sure the studio and the network were hard pressed to keep him on the show for that very reason. Jennifer Lien was the runner-up and so ultimately she was let go, and Jeri Ryan was brought in as Seven of Nine.
It's the nature of the business, I suppose. I don't think it was the right decision, but it's so far in the past now that there isn't too much point in dwelling on it. I think that the character of Kes was poorly developed in her 3 seasons on the show. They could have done more with her. Her unique Ocampan abilities and her short life span could have made for some really dramatic and interesting episodes (particularly towards the end of the series... the ship is getting closer to earth but Kes is getting closer and closer to death). I really enjoyed Kes's relationship with The Doctor and I think it would have been nice if it turned romantic (the two were definitely quite affectionate towards one another, and The Doctor would be a much better match for her than Neelix ever was).
Personally, if I had been in charge, I would have kept Kes around. There are a couple of ways this could have been accomplished:
Option 1 - get rid of another cast member. Harry Kim was the obvious choice, but for political/marketing reasons, Garrett was given a reprieve. I think Neelix should have been the next in line. By the 4th season, his character was not necessary. He served no vital function. He was originally brought aboard to be a guide for Janeway and the crew, to help them navigate through the Delta quadrant. But at this point in their journey, they had moved beyond the region of space where Neelix could be helpful. The character was relegated to comic relief and he didn't do much to add to the series. I think the only reason he remained on the show was that he was the "weird alien". Every Trek series seems to want one really odd alien with a lot of makeup and/or prosthetics. TNG had Worf. DS9 had Quark and Odo. VOY had Neelix. (And ENT would go on to have Phlox).
Option 2 - bump Jennifer Lien (or another cast member, like Ethan Phillips) to recurring. They don't have to appear in every episode. They don't get paid like a series regular. But they can still remain with the series and contribute several times per season. DS9 did this quite successfully with their broad range of recurring characters, like Nog, Rom, Dukat, etc. There is no reason why Jennifer Lien had to completely leave the series. Just simply agree to use her in half the episodes instead of all 26. She can still remain with the show and the character of Kes can be used on an as-needed basis. This way she can still develop and grow.
I think that introducing Seven of Nine was a smart move. She definitely injected some energy into the series, and she was a welcome addition to the cast. Despite her appearance and being written off as a "Borg Babe", she was actually an interesting character and had more going on for her than her catsuit. So I don't think it was a foolish decision to introduce a new character in season 4. Firing Jennifer Lien was unfortunate, and didn't need to happen, but sadly that's how things work.