Encrypting a compressed audio stream does not add to the bandwidth, aside from the initial key negotiation.
Furthermore, the bandwidth required for audio of a quality that's indiscernible from the original is negligible when compared to the bandwidth of Bluetooth radios. Ridiculously good audio is 320 kbps, and Bluetooth is easily good for 25 Mbps.
I suppose you could argue that the battery power used to perform this computation is the limiting factor, but a good embedded DSP used to perform the recording and transmission typically have tiny power requirements and hardware encryption routines that don't significantly change the power requirements of the device, as compared to keeping a blue LED blinking or powering an earbud speaker.
No, let's be honest here. The actual limiting factor is engineering time and money that goes into developing these devices as quick and cheaply as possible.
I understand that this leak is related to mongodb... and that is terrible, but mostly referring to your bluetooth example.
I mean take bluetooth headphones they are notoriously insecure, but the range in which eavesdropping could take place is pretty small, and for most of us you would just be eavesdropping on our annoying music. Seems reasonable that they save bandwidth on secure transmission of data for higher audio quality. That said I could see an argument the other way, but I'm sure there are more examples where it doesn't seem like a big deal. It would be interesting to hear from someone who thinks I'm dead wrong.