VI also pulled the split party mechanic but it was more of a short diversion.

It works better in IX than XIII if only because IX's classes are hardwired in whereas XIII's is slightly more fluid with the paradigm system, making the issue of getting a new party member in IX a bigger deal than it was XIII. Getting Fang was not as game changing as getting Freya for instance because Freya offered something completely new and different in terms of abilities and role in your party whereas Fang is a bit less special since you already have people who can do the same roles as her with only a three stats and some abilities creating any kind of variation. Even latecomers like Amarant and Eiko offered new dynamics to the party whereas the different ways each of the characters utilize the Paradigm Roles in XIII are pretty subtle and often still made many characters second rate compared to better options within the party.

It's the same reason why the switching party mechanic worked better in FFIV and VI because the characters did change the way you play the game. The biggest game changer to enter your party was getting Snow back as the player had been denied the Sentinel class and gaining that job finally ended most of the cheap leader kill deaths in the game. Of anything, I would say XIII is closer to IV, where the limited party options were meant as a means to keep the player on their toes because you didn't always have the same options. IX is probably closer to VI where new character introduce new moves and playstyles that change up party dynamics and options.