Regular MQTT sensors have an expire_after option. This option is not available for MQTT Binary Sensors.
It would be handy for things like motion sensors that do not send an update when motion stopped. I currently have to create an automation for each MQTT motion sensor to reset its state back to off after 5 seconds. With this expire_after option this could be accomplished much more easily with a simple configuration line.
It may have just been over looked. I could also be wrong, but I looked at the documentation and it doesn’t mention it. It also appears to be missing from the source code.
No clue, it depends on the base class used to communicate with the device. If it doesn’t exist, someone needs to create it. Adding into the component python file would be very easy.