Earlier quoted context omitted.
These systems are using ADS-B and are only designed for operational/informational purposes so far, as far as I know. They are not used for air traffic control or other safety-critical purposes.
If it's using Iridum or (more likely) Inmarsat, it would technically be ADS-C. (There is also a parallel system that allows satellites to detect existing ADS-B signals, developed by Aireon - but this is relatively new and not used globally.) These absolutely can be used for air-traffic control. ADS-B has better temporal resolution than radar, and ADS-C is at least as good as manual position reports over the radio (us…
ADS-C is a two-way communications protocol; ATC can request a certain update interval and I believe also boundary conditions requiring extra location transmissions. If that communication fails, both the ATC and pilot are informed about the fact, and they can reliably switch to other means of communications (e.g. voice position reports over HF).
> These absolutely can be used for air-traffic control.
ADS-B is (at least for now) mostly an augmentation of primary and secondary surveillance radar, as well as something to give other aircraft better situational awareness (via ADS-B in), as I understand it. I don't think either ATC nor pilots are currently relying on it for safety-critical decisions.
The big problem is that it's always possible for some plane's ADS-B transmitter to fail (maliciously or otherwise). On land, you have secondary or primary radar to fall back to.
This applies doubly so to third-party (i.e. non-ATC/non-AOC) satellite-based relaying services, since not only the ADS-B transmitter can fail in that scenario (and ADS-B was not originally designed to be received by satellites), but the relay service could fail as well, and the failure mode would be much less visible to both parties than in ADS-C.