Because transmissions are unreliable. If you're over the ocean there is no ground to send your transmission to. Black boxes store considerable amounts of data - telemetrics, voice recordings for the past two hours...stuff that to be useful you really have to stream.
So the only viable option for streaming that kind of data is over a satellite link, except it should come as no surprise that when you most need the data the uplink won't work (maybe something ripped the fuselage and damaged the transmitter, power was lost, you no longer had line of site to the satellite because the plane rolled, etc).
There's no benefit. You are going to be sending people out to the plane anyway. If the plane is under the ocean you're going to investigate regardless. Flight recorders are designed to last - the Air France 447 recorders were finally found two years later, 4000 meters under water. Data links are unreliable, not there when you most need them, and not worth the trouble.
> There's no benefit. You are going to be sending people out to the plane anyway.
This is a fantastic point. I can't think of many accidents that were resolved by the FDR alone. The FDR tells a substantial part of the story, obviously (flight control positions, instrumentation data, etc), but the wreckage suggests where potential points of failure occurred. The importance of this cannot be understated, and I'd highly recommend watching (albeit rather dramatized) Crash of the Comet [1] and related videos for how important wreckage and metallurgical analysis has been in resolving otherwise difficult accidents.
To add to your comment, the FDR and CVR have demonstrated that they can function up to the point of impact (with some exceptions, such as a few accidents caused by severe in flight fires), which yields some very important telemetry as to the attitude of the aircraft, state of the engines, etc.
So the only viable option for streaming that kind of data is over a satellite link, except it should come as no surprise that when you most need the data the uplink won't work (maybe something ripped the fuselage and damaged the transmitter, power was lost, you no longer had line of site to the satellite because the plane rolled, etc).
There's no benefit. You are going to be sending people out to the plane anyway. If the plane is under the ocean you're going to investigate regardless. Flight recorders are designed to last - the Air France 447 recorders were finally found two years later, 4000 meters under water. Data links are unreliable, not there when you most need them, and not worth the trouble.