Yeah like bitmessage, but the network overhead (all users see all messages) of bitmessage might be prohibitive for battery powered clients, no?

Probably not a huge deal as phones become more and more powerful.

I don't see how its not a big deal.

If all messages are seen by my phone, just to be inspected and discarded, then my phone is consuming bandwidth and processing cycles on irrelevant data. And unless my phone has free bandwidth, and the processing cycles don't consume power (or it has infinite power), how can it ever not be a factor?

It'll get figured out.