I am against giving up my land-line telephone for two reasons: safety and redundancy.
As far as redundancy goes, I am an untrusting person towards technology, both new and old, though I trust our old phone lines the most. We live far enough out in the country that cell service is not reliable, and neither is electricity. Assuming that cell service actually penetrated our house far enough to allow for reliable calling at our convenience, one would still need to maintain a charge on that phone. This requires electricity. We have had electrical supply interruptions in the measurement of days in the past. Poor preparation and/or a lack of a functioning generator could cause issues with convenient, reliable cell phone usage. In comparison, old-fashioned phone lines maintain their own power that is separate from the electricity grid. Those phone lines are buried (unlike the power lines), so are more reliable during storms and other natural disasters.
And once I start talking about natural disasters, I also have to talk about personal ones. To me, the more important part of having a land line is that anyone in the house can use it at any time. Our phones are in logical places around the house (kitchen, living room, bedrooms), and can be easily located. And those phones work without special instructions*. Small children can use them, as can panicking adults. I expect my guests to be self-aware in times of crisis, and to be the ones to call 911 if I need help. I do not expect guests to know where an unlocked and functioning cell phone is hiding when there is an emergency in the house, and where they have to stand in the house (or yard!) in order to maintain reasonable reception. Additionally, a land line has caller ID which is tied to an address. Our local county rescue teams are not all that modernized, and their system is still optimized for land-line responses. If and when I call 911, I would like the police/fire/rescue to be able to find my house even if they can't understand what I'm saying.
So no, I have no intention of canceling my land line. I won't do it even if AT&T comes out and puts a transmission tower across the street and we can get cell reception 20 feet underground. I like the security of knowing that there is as close to a "red phone" in my house as a common person can have, and anyone can use it.
While I do not have children, I encourage the friends of mine who do to consider what safety measures they have put in place for if/when something goes wrong and it is left to the child to make the life-saving phone call. Is there always a phone available for your child to use? Is it honestly accessible to that child's age and skill level (as well as height and physical skill)? Thanks for considering it...
* Yes, we have cordless phones. But when we have power outages, we plug in our collection of old corded phones that do not require any external power sources.