One thing I don't agree with you - lacking any exact numbers based on what you said - is that we won't be around by the time a message we send to an ETI gets a response back to us. If they are in the Virgo Cluster, maybe. But if they are anywhere near us (if there are 1 million technological civilizations in the Milky Way galaxy as Sagan once estimated, then the nearest one on average is 200 light years from Earth), then we as a civilization could have a long but actual conversation with each other.

I was discussing this one particular method where we are able to send a very narrow message, only in the exact opposite direction of any handy pulsars. These beams would be very lucky to intercept any useful planets within 200ly. Certainly they would intercept very very few.

That makes it less useful, by my standards. That makes it less likely that anyone is using that method to send, by my reasoning.

There are some great ways to listen-to/send-messages-to all the stars within a 200ly radius. Those methods - in my estimation - are worth pursuing.