Doing the math on the I love you dad shirt square law and distance to nearest stars you will (hopefully) notice that even such “large” output signals coming from a nearby star would be essentially undetectable by the time they got here. At only 4LY (roughly 3.784×10^16 meters) to the nearest star the signal would be attenuated by a factor of 1.4×10^-33. So the original kilowatt becomes less than a thousandth of a billionth of a billionth of a billionth of a watt give or take a few decimal places. Spell that out in your best Carl Sagan voice to get the full effect of how small it really is. If you had a gigantic antenna (or array of antennas) and you were looking in exactly the right place in the sky you *might* be able to pick that will o’ the wisp signal out of the background radiation, but probably not. Now you might argue that our noisy neighbors would be shouting louder with much more powerful transmitters, but why would they? Their TV and commercial traffic would only need to be as loud as ours to reach their own people. And even if they were broadcasting many orders of magnitude “louder” at the origin it wouldn’t make much difference.
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