It's nowhere near that bad. Arecibo could communicate with a similar installation out to 21,000 LY, at least.[1] That's with a megawatt of power, less than many analog TV stations.
Seth Shostak, head astronomer for the SETI institute, thinks the actual number is 400 light years, not 21000 light years. And James Benford, President and Founder of Microwave Sciences (and twin brother of science fiction author Gregory Benford), thinks that 400 light years would be the range for detection, not for communication, pointing out that the ground-based receivers wouldn't be able to integrate the signal over enough time due to planetary rotation.
If we're still factoring in ground based solutions for interstellar communication I think we're assuming the wrong level of technological development. I'd like to see how it works out for a few dozen receivers positioned as far apart as possible in Solar orbit.
[1] https://www.seti.org/arecibo-message