You seem to be confusing the billboard device with the alternate mode negotiation. The billboard device is a normal USB device which shows up once the alternate

You seem to be confusing the billboard device with the alternate mode negotiation. The billboard device is a normal USB device which shows up once the alternate mode negotiation times out. The alternate mode negotiation happens on the configuration pins over the USB-PD protocol. The alternate mode discovery is initiated by the host, so the only way the hub could change which alternate modes it supports would be to disconnect from the host (unplugging all the devices on it, which would be particularly bad if some of them were storage devices). (Also, I believe HDMI alternate mode with USB 2.0 is possible. The only alternate mode I know of which changes the meaning of the USB 2.0 pins is VirtualLink, which uses them for USB 3.x instead.)