For air safety this could be NTSB or AAIB servers or wherever. ..... By putting the storage in the NTSB (or similar) it should allay the concerns that some pilots have of management misusing the data.
Are you really sure you, and other passengers, would wish to see airline tickets costs shoot up to support this, and the numerous cancellations / delays / diversion caused whenever the Satcom could not get/lost a "logon"?
Take ACARS as an example. A long standing system that (for me) only uses VHF in central Europe. Breaks / fails often, sometimes intermittently, sometimes for rest of flight.
These systems are not designed for safety, are "nice to haves" commercially, and some airlines just do not use them for cost reasons. it is a massive step to elevate them to "flight safety" / "No Despatch MEL items".