I still don't see why only a black box should be used for that. As long as a satellite uplink is powered by a separate external power source, none of these factors will stop a transmission.
There's also a practicality argument: when a plane is flying along normally, you don't need consistent satellite information - you've got radio communication, radio data-links, and controllers watching. So the usefulness of a satellite uplink only comes when something is not right with the plane.
If we're in that situation - that there's something wrong enough with the plane that you'd want to know about it via the uplink - what makes you think the uplink will still be working? Air planes are designed with huge levels of redundancy and overengineered margins: are you going to take all that, double it, and then put it into a satellite transmitter (which probably won't have that much data to send anyways if the plane is in that state)?
So no, I don't think we need constant satellite uplinks. Black boxes (especially ones of the newer generation) are very well-engineered, and the NTSB guys are masters at getting things off broken ones.