Just so you know how much data we're talking about, I did a quick check of a DFDR file I have from a six hour flight (I was investigating a strange engine anomaly on the flight). Six hour flight is a 150 meg file, or roughly 25 meg per hour (and that was an older DFDR, new models record even more). Multiply that by the thousands of airplanes in the air at any time and you're going to quickly overwhelm the available satellite resources. So $billion$ of new capability would be needed for the downlink.
25 meg per hour is 7 kilobytes per second (56 Kbps) per aircraft. Existing satellite internet networks can absorb that without breaking a sweat.
Also, most of this stuff is highly optional and it's stored mainly because it can be. 20 years ago standard FDRs on aircraft like the 777 had the capacity to record 64 or 128 words per second (0.77 or 1.54 Kbps). After the expansion of the list of required parameter groups in 2002, Boeing started installing FDRs capable of 3 Kbps.