I don't want my desktop client to wake up my mobile because I wrote a message. If you send a message, I don't think you immediately need to know that on every device.
But the sent carbon can also remove the blinking notification on my phone from the previous incoming message, so I don't have to wake up the phone to see if there is actually something new!
Ge0rG is right and I won't do this until chat markers (XEP-0333) are supported by every chat client because chat markers would make the behaviour described by ge0rg unnecessary.
CSI with mod_csi_simple is included in Prosody since 0.11 and follows Ge0rGs line,
pushing your own carbons to inactive devices.