It would slow down game play.
Cyclical initiative means initiative doesn't change all that much. (Gee, I'm Mr. Obvious today.) So there's no need to change the init order at the beginning of every round.
Generally, players decide what they want to do as other players are taking their turns. However, if initiative changes every round, players have to make their decision at the start of every round without the ability to change their mind depending on what is happening to their friends. Even issues like "who gets to talk first" can complicate things.
I can picture a really bad scenario happening because of this:
Fighter: wielding greatsword, had a good init roll. "I'm slicing open the troll. Heh heh. I hit AC 28, dishing out 23 damage."
DM: "the troll rages, striking AC 30 and 34 - those both hit, right? That's 60 damage, and now for the rend ... that's another 41 damage."
Fighter: "Yikes! I'd like some healing here!"
Cleric: "Um... I already decided to cast searing light at that lich in the background. If I were to move up and cast heal, I'd have to move back three init spaces. Maybe I can ask the DM..."
DM: "No. The lich is only one init point behind you. I guess you do it, but that means you have to let the lich go before you."
Cleric: "Okay, sure."
DM: "The lich is casting horrid wilting. He had made the decision to do so at the beginning of the round - that's why he's so late. How many hp are you at again, fighter?"