Or why it is still one large black box, but not, say, 20 orange 64GB flash drives, which fall all over the place?
An aircraft costs hundreds of millions and 20 flash drives cost peanuts. And it is not a problem at all to write to several flash drives simultaneously.
There are obviously going to be problems wiring data (or certifying a wireless solution) and, more importantly, power to 20+ disparate locations (you want them spread out, right) on the plane, but the big one, IMO is the survivability standards.
Every "black box" is required to have a certain amount of fire, impact / shock, water-pressure etc. resistance. They are also required to have a ULB (pinger, for underwater location) with 30 days battery life (maybe soon going up to 90). All the casing to do that, and the pinger, and the chassis that is supposed to keep them together under the same test conditions, ends up weighing quite a lot (for an aircraft component). Inside it all, these days, is basically a small flash drive - bit higher than consumer spec for survivability, and hence more expensive, but that is all it is.
20 black boxes to meet current regs is too heavy and too expensive, so your problem is changing the regulations. 20 slightly less survivable black boxes that could therefore be much smaller lighter and cheaper sounds great - except for the risk that you then find them easily but the data hasn't survived.
That brings us to the biggest issue - the current standard black boxes are almost always found, so where exactly is the problem you are trying to solve. Real-time data streaming would solve a problem by eliminating the search for the wreckage entirely - arguably saving a lot of money in some cases. Except that not every insight comes from the black box, investigators conclude a lot directly from the wreckage - so I reckon you need to find it anyway.
Real time _location_ streaming (doesn't take much data) plus fully survivable black box is probably the best compromise, significantly shorten some search times - and that is what is going to happen.