Assuming that the FFTs handle independent slices of data (as I can't see why you'd go back to the time domain), the data throughput they're handling is 2048 * 1

Assuming that the FFTs handle independent slices of data (as I can't see why you'd go back to the time domain), the data throughput they're handling is 2048 * 15 bits * 80 Hz = 2.5 Mbps. That may sound like a lot, but it's not unprecedented and it does not require huge power consumption; think of a USB connection hub or perhaps an ethernet hub. Actually the thermodynamic requirements of that sort of computation are much much less than the practical requirements; at room temperature the minimum power to handle that bandwidth is only 3 × 10^-15 watts; the FFT doesn't need to add to that because the FFT is a reversible computation. We're a long way away from perfection in this sense.