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The pont is, it takes many, many times as much power to transmit a radio signal than to receive. And then don't forget that the BT antenna is omni-directional. It needs to transmit enough power for the receive to be anywhere in the room, so the vast majority of its power is just wasted.
That is not true.
Cellular basestation transmissions are directional, using a variety of technologies. Some, use sectored (180, 120, or 60 degree sectors) directional antennas, others use beam forming techniques through signal processing. The greatest capital cost in a cellular basestation system are RF power amplifiers, generally representing 30% of the overall cost. Transmitting omni-directionally wastes power, requiring larger power amplifiers and greater electricity usage. It's just not done.