Well, this falls into my court, as an IT guy who does VHF and HF radio as a hobby.
The black box records lots and lots of data, including the voices from the cockpit, all the monitoring data from the instruments, settings of controls, airspeed, etc.
Airplanes typically don't use HF radio at all; most of the ATC (Air Traffic Control) conversations happen over VHF, which is short range. There are only a limited number of VHF channels available, and they are all full already, with voice co-ordination of the aircraft movements and status.
Since VHF is short range, it wouldn't do any good to send data over it anyway, for flights going over the ocean or unpopulated areas.
HF has more range. But with that range, you get limitations on data bandwidth; you can send digital data, but it is very low capacity, and error-prone. It's hard enough to send one voice stream, and there's lots of technology in use to get that through.
There's no way to get a huge amount of data through those pipes.
Now that there are satellite links on planes, that's an option. But that's new technology, and actually quite expensive, and it has bandwidth limits too. And outages.
If you've ever used the inflight wifi, you get a sense how limited it is.
I imagine they will move to satellites over time, if it gets cheaper. Just realize that the major airlines have a commercial interest in fitting their planes, and it's taking them years to do their fleets.
As you pointed out, the crashes are rare, and the black boxes are there mainly to determine what happened after the fact. Since the investigations take months and months anyway, they figure they can wait.
