https://www.ti.com/lit/ds/symlink/tps65987ddk.pdf?ts=1688854016963&ref_url=https%253A%252F%252Fwww.ti.com%252Fproduct%252FTPS65987DDK
The power input port on USB-C docks can only be used for power input.
The reason why USB-C power input ports can only be used for power input has a lot to do with how the USB protocol works. USB was designed from the start as a master/slave protocol with one master device and many slave devices. This was enforced by using type "A" ports on the master device, and any hub ports that faced "upstream" to the master, and "B" ports on slave devices, and the hub port that faced "downstream". With USB-C this mechanical enforcement of roles was lost but the "upstream" and "downstream" roles remained. There are USB-C ports that can act in either role but to do this requires extra electronics.
What USB-C also added was "alternate modes" that used non-USB protocols, and added a more complex power delivery. The alternate modes doesn't play much into this but the roles of each connected device and the power delivery methods do.
When a USB device is connected it's the master that is expected to provide power. With "A" ports always being the master it always provides power. With USB-C there's a handshake protocol on determining who is the master. A laptop is a master on a USB bus, typically. Also what is a master is a USB-C power brick.
There can be only one master on a USB bus. The way this is worked around on a USB-C dock is that the USB-C functions are split inside the dock so that the power master is on one USB-C port, the power input only port, and the USB data master is on the other port, the one to the laptop. The power input USB-C port then has no USB data connections, only the connections required for power delivery. The dock is then a middleman in the power delivery portion of the USB-C connection, effectively serving two masters.
Going deeper into this we can see that the USB-C connection consists of three data paths. There's the power path, the USB 2.0 path, and the "superspeed" path. The "superspeed" data path consists of four pairs of balanced wires that can be used singly, in pairs, or all four together for USB 3.x, video, Thunderbolt, or some other alternate mode data. The dock takes these three paths and breaks them out into the various ports on the dock. The power path goes to the USB-C power input port. The USB 2.0 and USB 3.x paths go to USB-A ports. If there is a video path, most often DisplayPort but it could be MHL, goes to a video port. The controller chip in the dock then has the laptop be a data master but power slave.
If the dock has ports other than power, USB-A, and video then these are often just USB slave devices embedded inside hanging off the internal USB hub. Such internalized USB devices are often a flash card slot or Ethernet port. The video protocol from the laptop to the dock is almost always DisplayPort but the video output can be HDMI or VGA with the use of a video conversion chip. But perhaps I digress too much from the point.
The point is that because USB is a master/slave protocol the functions of two USB-C ports on a USB-C dock has to be split up to allow for more than one master. The laptop is the master of the data portion and the power brick is master of the power portion. It's rare to see more than two USB-C ports on a dock because the USB protocol doesn't really allow for more. If a dock has more than two USB-C ports then the other USB-C ports will have some limits on the port functions to avoid having to deal with more than one master, or the dock is using a more complex protocol like Thunderbolt that is not master/slave but peer/peer.
If a USB-C dock or hub supports more than power input on a USB-C port then it would say so, because adding that would be expensive and they'd advertise this to justify the expense. In theory it may be possible for this power port to act as a power output port as well as a power input port and not violate any USB protocols or specifications but that adds complexity that few people would care about. If people want power output to charge a cell phone, as an example, then they can use a USB-A port for that.