What I find strange about this (common) question is that nobody seems to remember what they did before mobile phones. I got my first mobile phone in 2001, but it's not like I was chained to my house from birth until 2001.
I admit I might be more wary if I lived in a suburban or rural area where I could end up broken down in a car miles from civilization. Then a phone is a nice backup.
The $0.10 minutes that come with that aren't especially competitive with other prepaid services. I'm not sure they will activate a phone everywhere.
But the 'have a working phone' baseline isn't all that inconvenient or all that expensive.
The phone simply being turned on doesn't equate to more calls being made. Like the parent said, turn it on when you need it.
"The FCC's basic 911 rules require wireless service providers to transmit all 911 calls to a PSAP, regardless of whether the caller subscribes to the provider’s service or not." http://www.fcc.gov/guides/wireless-911-services/
Doesn't cover calling a tow truck, AAA, or a friend or relative to come pick you up. But if you only use the phone for real life-threatening emergencies, you don't have to pay.
I can't off-hand think of anything where contacting me personally would be required in an "emergency situation", if it's really an "emergency" there's probably better qualified people to call. This is colored by my situation, I'm not a parent, I'm not the sole decision maker for anything mission critical (either personally or professionally). I'd be sad (or sadder) if my Mum or Dad died and I missed out on saying goodbye because nobody could contact me immediately, but they live 5hrs away from me so that's a pretty unlikely scenario.
I'm kinda "at peace" with spending time "uncontactable" anyway, I spend at least an hour a day (and sometimes 8 or 10 hours) on a motorcycle - where I might feel my phone ringing in my pocket, but I don't answer it until I've got to where I'm going and stopped the bike. I also treat the phone the same way in movies/restaurants/gigs/meetings, and often while deep in something complicated at work.
Personally, I don't buy into the idea that my phone is so other people can reliably contact me immediately in case of emergency. When work wants that, it's called "on-call" and they pay me for it. In my personal life, I answer my phone if and when it suits me, and I'm not enslaved to anybody who happens to have my number.
I've found out that most times when I "urgently" want to get a hold of someone - leaving a well thought out message works out just as fine.
I honestly can't believe it when people ask that question. It's such a scare tactic.