Actually, ham radio operators do exactly this. They literally send out messages out into the ether with the hopes of someone replying.
QSL: https://rsgb.org/main/get-started-in-amateur-radio/operating...
We do that all the time, in as many ways as we can think of. From the top of my head:
- amateur radio
- sending lasers signals to the moon and waiting for it to get back
- chatting with random strangers on internet
- the Arecibo message on space
- SETI is basically trying to catch an alien "hello"
- sending "messages on bottles"
Really, sending "hi" in imaginative ways for no reason is a very human thing to do
https://en.wikipedia.org/wiki/The_Forge_of_God
and
https://en.wikipedia.org/wiki/Anvil_of_Stars
Anvil of Stars is often said to be the weaker of the pair, but it haunted me for several reasons, not least the extremely spooky ending!
In the books game theory means that the most prudent way to deal with a competitor species is to obliterate it immediately on discovery. The answer to Fermi’s Paradox is that everyone is keeping their heads down and and hoping no one notices them.
Humans, on the other hand, are merrily broadcasting away without a care in the universe...
For all we know, the universe is jam packed full of Predator-like aliens who are the dominant species on their planet specifically because their society is built around dominating everything they can.
Your point doesn’t really hold up if the effort to destroy a civ is basically zero, while the cost to defend is approximately unachievable.
Like plaguing Picard and crew on the USS Enterprise.
Not only is there likely an ideal, optimized way of sending information long distances, I suspect there also a very limited number of things a matrioshka brain would care to broadcast or receive, like the values of some fundamental constant.
Saying "hi" for fun to other civilizations isn't even something we do on our own planet with our own people. We only talk to people for specific reasons, even if we're unaware of those reasons. We'll go out of our way to avoid a homeless person's greeting rather than risk learning something about/from him.