Iridium has 66 sats in low polar orbits, giving them 100% coverage of the Earth's surface, Inmarsat used geostationary orbits and has coverage of most of the Earth within ~80 degrees of the equator. In the MH370 case, the last communications received were from the Inmarsat terminal on the plane. The problem is that the signals didn't have location data, and the services that would provide locations were disabled.
As most countries migrate to ADS-B, there will be more planes regularly transmitting their current location. There is also an ongoing effort to add ADS-B reception to the Iridium network so they don't have to rely on ground stations.
The only real changes that are needed now is to make sure transponders can't be turned off in flight.