Why bother with complicated satellite connectivity when you likely have a smartphone in the pocket? For one thing, the FCC has banned the use of cell phones aboard aircraft per 47 CFR 22.925 l. Originally, it likely had to do with the way the cellular system works.
As the name implies, geographic areas are divided into different cells which use different frequencies, and no two adjacent cells use the same frequency, but two separated cells can safely share them. A phone in a plane has a much longer reach than a phone on the ground, so it could tie up a single frequency across multiple cells. Furthermore, the phone may not be able to receive a signal at all with multiple cells using the same frequencies.
On top of this, cellular network providers use antennas that aim their signal toward their users. As there are no users above ground, the antennas are tuned to radiate most of their power horizontally rather than upward. Additionally, the floor of the aircraft could have a few sheets of aluminum between the phone and the cellular towers, which will further attenuate any signal.
This means cellphones in aircraft are not likely to work well in many situations. The lower the aircraft, the more likely the phone will be able to send and receive an intelligible signal. In less densely settled areas, where there are fewer, larger cells, a cell phone is likely to work better. For some flights it should be possible to maintain a full 3G or LTE connection, while others probably cant even get a basic connection.
What about safety? Cell phones emit radio waves in a variety of frequencies from about 450MHz to over 2.1 GHz at several hundred milliwatts. A general aviation pilot flying with family has likely had cell phones left on during flight and, to our knowledge, there are no recorded accidents attributed to cell phone interference. We know of at least one, ahem, instance in which a pilots phone was inadvertently left on. The worst interference ever noted was during a flight for this article when a passenger left a cellular phone on and placed it on the glareshield just over the audio panel during a check of the Iridium Go. A distinctive series of clicks was heard over the intercom, which was almost certainly a GSM handshake.
In late 2013, the FCC chairman suggested modifying the rules on in-flight cellular use. So far, nothing has come of it. However, if the FCC lifts its ban then the use of cell phones in general aviation planes would then be at the discretion of the operator under FAA rule 91.21. It could also squash sales of satellite transceivers.