Not a bad idea, but ...
Like anything else may the day come when the classic boxes become history, ... or at least secondary.
Increasingly more and more airframes are outfitted with full (and very fast) Internet connection available to all passengers for a "nominal" fee.
These connection are close to common place on intercontinental flights.
Why can real-time data not be transmitted using the same system?
If a passenger can afford to sign up on a flight by flight or contract basis, one would think the air carriers could as well.
Heck the could make it a simple condition of a business agreement with the provider.
What bandwidth is required for flight and voice recordings.
Not much I venture.
I have streamed HD video on board and tested connection speed onboard and the results are pretty good.
The first objection is probably that Internet is not always 100% reliable.
That would be true, however, most interruptions can be corrected in a fraction of a second. Second, till proven reliable leave the boxes in place.