@ rgbrock,
No, addressing is a simple matter.
The issue is that you cannot have a large number of transmitters each sending continuous streams of data at random because the receiver in the satellite would just receive a meaningless jumble of signals. There has to be a system of control that determines time or frequency slots for each packet of data so that it can be individually resolved and identified.
The cellular phone in your pocket is at all times controlled by the base stations telling it from one millisecond to another when to transmit and when to receive, which do not happen simultaneously. A similar thing already happens with satellite phone and data systems, but they were designed to communicate with limited amounts of data usually from static or slow-moving terminals.
The envisaged data from aircraft monitoring would be fast and continuous. With fast data the length of each data bit is very short, with time periods less than the time taken to travel from plane to satellite and return. The variable doppler-shift due to aircraft travel is also significant, placing system constraints. As stated before none of this is impossible given sufficient resources, but large volumes of data from many aircraft cannot just be bolted on to existing systems.
There are many online references to FDMA, TDMA and CDMA which will explain the concepts if you want to go into the details.