"That's why the black boxes cannot transmit any data."
I know this is going to sound pedantic, but the black boxes are sending a datum, as in the ping. They could easily be modified as you intimated to morse a fleet ID, which under ideal conditions would be helpful, but under poor conditions could be next to useless. However, the idea of a morse modulation would parallel the SETI model of looking for intelligence amongst noise, which seems to be the situation ATM.