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.
Telemetry isn't as easy as one might think. Airbus, AFAIK, is one of the pioneering manufacturers in this regard, as we witness in the crash of AF447, but given the amount of data that FDRs record, I'd imagine it wouldn't be a simple feat.
And in part, the reliability of FDRs and CVRs has been such that a comparatively small number of those recovered were void of retrievable information. So my guess is that replacing them would require satellite links (which obviously exist) but 1) have complete coverage of the globe (remember, aircraft like the 777 have a huge range) and 2) would be recording real time flight data for every single aircraft in the air. Then you have the issues of costs, approval from the various industry regulators (FAA, etc), and probably no less than 5-10 years before acceptance. And that's being hugely optimistic. In many ways, there's a point where carting around your telemetry-recording device is actually the cheapest and most effective method. It's counter-intuitive to some, but again: Telemetry isn't easy. Or cheap. And it needs to be reliable.
It does appear that Iridium Satellite is proposing something of the sort [1]. And trawling the Interwebs yields some [2] interesting [3] discussions [4].
But chiefly, I think the limitation is mostly cost, and as objclxt points out, reliability is another issue that would need to be addressed. There are a lot of planes in the sky. [5]
The critical data for accident investigation is acquired during and after an incident of some kind, which by definition precipitated or was precipitated by system failures. The failsafe data store in a failure condition is by necessity local.
I don't have a ton of information to back it up, but I imagine they record a ton of data and it would require a pretty constant and huge data transmission from the airplane to get it all to the ground in near-real-time.
