If they were doing E2E encryption, that would not be a problem. Broadcasting to find the right recipient (the one with the decrypting key) but contents protected from everybody else.
Ok so how would key distribution work here? Tofu?
If you can meet once physically, there is nothing better than that to exchange your public keys. That's why hackers meetings are "public keys signing parties".
For something as low latency as messaging, you can probably use proof of work for DoS resistance
Because messaging software that drains batteries is what everyone wants...
It's better than the alternative, which is no messaging.
PoW or no messaging seems to me like an obviously false dichotomy.