There's a major issue I believe is relevant to Sat Phones: they require large amounts of battery to operate, so you essentially turn them on to call, off to save battery. Unless you are in one of them 4-by's and have lots of juice and don't worry about such things.
So from the standpoint of carrying one for someone to reach you in case of emergency (your parents), there's that issue of how and when they reach you when your phone is generally off in order to conserve battery power.
Email works just as good - you can general check it daily, which works just as well as saying 'call me at such-and-such time and I'll have the phone on' (except you changed time zones again and no one knows that).
And even if there is an emergency at home, you have to work out the details for catching a flight home, leaving your bike and gear somewhere - takes time, and by the time you sort that all out...well, the emergency nature of the situation may be well past.
Cell phones in general:
in case
you have an emergency - who you gonna call?

Are you carrying a directory of the nearest road service/hospital/police agency/embassy? That's a lot of directories to pick up when you're traveling hundreds of kilometers every day. And worrying about having those numbers available in advance is, in my opinion, way too much pre-planning detail to sit and worry about. You figure it out as you go.
It would seem that calling home to tell someone 'you have an emergency' is counterproductive - makes the folks at home worry and doesn't accomplish anything - who they gonna call? You're better off just leaving the phone off, thinking through the emergency - or getting to the hospital first, finding out the situation, then making phone calls - but then you can use a land-line/regular cell-phone/skype instead of carrying that Sat phone around - just more weight, more cords/chargers and expensive electronics to carry around and keep track of.
You'd be surprised to know how many overlanders don't carry a phone. Worthless, time-wasting/money-pit devices if you ask me.
Just a couple weeks ago, I was in Lago Pasadas, Argentina (in Patagonia near the Chilean border - Paso Roballos to Cochrane, Chile). On the wall of the hostel was a framed newspaper article, about the phone finally coming to Lago Pasadas in 1999!
Today its an emergency. Before phones, people probably had very few emergencies. Now, people call 911 because the neighbor's dog is barking.