A full dump is about 35 meg. Transmitting realtime is not alot of data at all. Satcom is very secure and the data is not really much of a security issue.
This in my oppinion is on the way as hardware like gatelink is becoming more common. The more computers we put in our aircraft the more data there is for us to update the computers. Satcom and irridum transmissions are solid and will probably be used for updating in the future.
The other thing to add is FANS, the motivation for FANS is supposed to be to increase air/ground communication accuracy, especially as aircraft overfly forign territory to reduce the safety issue of miscommunication. In all actuality the real Future Air Navigation Systems will be tied into FMS allowing ATC to command and control an aircraft. Pilots are slowly being replaced by technology.
Back on topic, constant data transmission at this point in time is not cost effective but absolutely possible. It would be great to have it set up where an ACARS systems message triggers an acms data stream say for 5 minutes then cancels if all parameters seem normal and further failures do not exist.