You are correct that cell service is often the first to go down. Depending on the emergency, many times it is simply due to the service being stretched beyond normal limits as 1000's of people try and contact each other.

Other times the cell infrastructure (towers etc) is damaged and needs repaired or replaced which can take days or weeks. On the other hand, many cell companies have portable cell towers and related infrastructure that can be quickly dispatched and made operational within hours or in a few days depending on location etc. The most recent example of this were the floods in Australia and which the Telco's deployed portable cell towers within days whereas those who were completely dependent on land lines were expected to wait up to months for landline service to be restored.

So as you can see, depending on cell service is NOT wrong thinking and there are advantages and disadvantages to any service. Cell phones have saved 1000's of lives over the years and I don't expect this to change anytime soon.

Also the smart and prepared people keep multiple and diversified types of comms in their kits that will allow them to make and keep contact in the event that one or more phone services are not available.