There are others here that probably have actual and good experience to answer this better than I (I am particularly interested in what Cam has to say). I have an SSB and use it, but mostly for fun.
I think that in relatively short order, satphones will become as prevalent as cell phones, and once that happens SSB will become antiquated (dare I say it). Sort of like Loran and GPS. One of the things you'll get with good reliable satphone service is Internet access. Once you have that, you have access to weather and obviously all the information you possibly can handle on any topic, not to mention actual videophone capability (it's there now with Skype). That's more than you ever can hope to have with SSB.
As to the point about "broadcasting," don't forget, with a satphone you can call 911 (literally), and the Coast Guard always answers the phone. Also, to the point someone made about there needing to be someone to answer the phone when you call, the same is true on SSB; someone needs to be listening to the channel you are broadcasting on. Granted, there are emergency channels, but users do not monitor these constantly just because they have an SSB onboard.
Another comparison to make too is VHF and cell phones. VHF still is used, but it's used a whole lot less because of cell phones. Indeed, radio the coast guard today, and the first question you get is whether you have a cell phone on board that can be used to call them or they you. That tells the whole story right there.
For the immediate time, however, satphone service all at the same time is (i) too unreliable, (ii) not fast enough for Internet, and (iii) too expensive to replace SSB just yet. But that day is coming, and with very few exceptions I bet just about everyone on this board will live to see it. Just my opinion.
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