There is an advantage of connecting a PS4 directly to an HDMI input on the C9. That is, if you don't want to change the picture mode every time you switch to the PS4.There's no benefit to plugging the PS4 directly into the C9 since it doesn't support any HDMI 2.1 features.
If you connect everything to the C9 via a single HDMI input, then all the devices connected to it will share the same picture modes (and their settings + selected picture mode) because picture modes are specific to the HDMI inputs.
Normally you want to use the game picture modes for both SDR and HDR on a PS4 but don't want to use these modes for your other devices like BD players or streaming boxes. Especially if you have a calibrated mode for movies.
Even if the PS4 supported HDMI 2.1 ALLM, you would still have to change the picture mode if you specifically changed some settings (gamma, colors, brightness, contrast etc.) for the game modes.
However, if you connect your PS4 to a dedicated HDMI input, you can set this HDMI port to game mode and the picture mode will automatically change when you switch between inputs.