There are indeed satellite phones in Nepal, but they are extremely rare given the number of people that have them vs. the number that don't.
Also, if you think the cell network can get overloaded in a hurry, you should look at the bandwidth budgets for those type of satellites. In disaster areas, sat phones have the same issue of 'network unavailable' when the birds are trying to pass more calls when they have bandwidth for. All commercial systems are allotted frequencies in one particular band or another and when they're full, they're full. Amateurs have at least a dozen bands, all with different propagation profiles. Not to mention, we have our own both voice and digital satellites that are exclusively for amateur communications.
Finally, in a supplement from Inmarsat's own 2013 shareholder report... 'The capacity of our satellites is limited and our network can be subject to congestion due to concentrated usage in a specific geography. Continuing congestion could damage our reputation for service availability and harm our results of operations.'