I'm sure you've realised by now that it's a daft idea, stemming probably from sheer desperation to have a more 'normal' life again.
I just wanted to address your point of "stuff happens rarely (fire, accidents, etc)
It actually doesn't. I'm an ofsted registered Nanny, and I'm also a "fast responder".
When a 999 call goes through to an area more than 3 miles (i think) away from an ambulance station, in remoter villages etc, we (volunteer and VERY highly trained) fast responders can be dispatched, and we get there and start to deal with the issue while the "proper" paramedics are on their way - sometimes it can take 90 minutes for a 'big' ambulance to arrive. The amount of times folk are taken ill in a pub/restaurant/road, or knocked over, or ANYTHING, is amazing. And scary, sometimes.
So if you're having a heart attack, or a stroke, or you've collapsed, or been knocked over, or anything, how the hell do we know you have three children at home alone? Say you manage to tell me you have kids - I'd assume there was a sitter with them (see sitters.co.uk for folk like me to help you)
If i realised they were alone, how would I get in? We'd HAVE to get the police and SS out - please, don't assume that nothing will happen.
Folk who died last night had plans for this morning. The ones in teh accidents this morning had plans an hour later. I'm sounding preachy, I'm sorry, but it is just not worth it.