This is where you are completely wrong. The scintillation of the interstellar medium will pretty much "chew" up any modulation (other than on/off), so SETI is doing just that. Looking foe an extremely narrowband CW signal (no information or modulation needed). And when I say narrow, I mean in the .8 Hz range. Just the fact a .8 Hz narrowband signal exists, denotes an artificially generated signal.
OK, I can buy that. So how much do we gain in signal strength advantage if we don't need to decode modulation? Could we pick up Pioneer 10 at 1 watt from 5 billion miles away? I think we just lost it recently and I thought it was around 5-7 billion miles away and transmitting at more than 1 but less than 10 watts.