Keeping the Bluetooth chip circuits permanently powered to listen for a “power-on” signal currently takes more power than their energy budget will provide. I am not sure what the limit is for the PPM, but checking a few recent TV devices from Philips I saw values around 0.07 to 0.15 watt power draw in their corresponding “off” mode, even when connected to mains power. See earlier request for this:
I don’t know if a future update to the drivers for the Bluetooth chip can fix that, or if they can reduce power use somewhere else. A Bluetooth chip in Bluetooth Low Energy mode might require from 0.01 to 0.50 watts, depending on what you are trying to do.