The HDMI input does not need to be active for DDC/CI control.
For example, a Raspberry Pi connected over HDMI can send commands even when its input isn’t currently displayed. It can change anything the monitor exposes through DDC/CI, from switching the USB KVM and configuring PBP/PIP to adjusting brightness and volume.
HDMI effectively becomes a limited out-of-band control path, opening up some interesting automation possibilities.