I think the fact that quite a few relatives of the missing ones are claiming the phones rang or are still ringing after the aircraft “vanished” needs to be investigated.
I'm a telecom engineer. What is normally called "ringing" is actually ringback tones. Unfortunately, there are situations in which ringback is erroneously generated. I think that if one was to try calling all the phones that were on board, 99.9% would not give ringback, but if any does, is false.
I’m no expert on mobile networks but given the laws that govern such things there should be a method by which global mobile operators could simply punch in an IMEI number into the database in order to determine the last radio mast registration. Collect IMEI numbers for all passengers and search through the databases. There’s nothing to lose. Even if one of them registered in the few hours after that plane went missing we would at least have a more accurate trajectory.
It is not so simple, there is no global datababase and while it is know that operator routinely log network registrations, there is no law that obliges them to do that. So since the most likely place where registration last occoured is Malaysia, it would be to their autorities to investigate using this method. For phones roaming from abroad, the home network would only know time, country and operator a give SIM last roamed in, but no other details.