Does USB-C Alternate Mode require the Billboard Device to be always connected?
Found the following in the USB-C R2.0 Spec 2019:


  When a device offers multiple modes, especially where multiple
  Alternate Mode definitions are needed in order to be compatible with
  multiple host-side implementations, successfully entering an Alternate
  Mode may be predicated on only one of the available modes being
  successfully recognized by a host.  In this case, the device is not
  required to expose but may still expose a USB Billboard Device
  Classinterface to indicate to the host the availability and status of
  the modes it supports.
  
  The host may send an Enter Mode after tAMETimeout.  If the device
  enters the mode, it shall respond with an ACK and discontinue exposing
  the USB Billboard Device Classinterface.  The device may expose the
  USB Billboard Device Classinterface again with updated capabilities.


According to this, exposure of the interface after Alternate Mode has been entered is optional, and may be re-exposed later with updated information if need be.  I will take this to mean "Yes, the interface can be disconnected" after Alternate Mode entry.