Satellite phones have to be used well clear of all obstructions, so that there's a clear path to the satellite. (You can't use a satellite phone indoors). They also require a great deal more power than a normal mobile phone and a dish to send the signal. (The dish serves two purposes. Firstly, it helps to 'focus' the signal, so that it can travel the 26,200 miles to the satellite. Secondly, it keeps the actual transmitting equipment away from the user's head, so that the high-powered radio signals can't damage the brain).
Those who are concerned about mobile phone masts being placed near to school playgrounds should actually be far more concerned that their children are using mobile phones next to their ears. (The brain absorbs far more r.f. energy from the phone next to the child's skull than it does from any transmitter at the top of a mast). If someone could invent a satellite phone which didn't require a dish (i.e. the transmitter could be held close to the skull, as with an existing mobile phone), the amount of r.f. energy entering the brain would be several thousand times current levels. (So you'd eliminate the almost imperceptible risk of brain damage from signals from the transmitter mast but replace it with an extremely high risk of brain damage from using the phone).
Using such high-powered phones would also greatly increase other safety risks. For example, if someone uses a normal mobile phone, while at a petrol station, there's a very small risk of an explosion. If someone was to use a much higher-powered satellite phone, at a petrol station, there would be an extremely high risk of an explosion.
Chris