They are extreme but they're all situations I've actually dealt with whilst babysitting or nannying along with suspected meningitis, parents stranded overnight in snow and completely uncontactable (I was ringing local hospitals), children falling from playground equipment or getting injured in games. Now I realise that doing it professionally puts me at a higher chance of coming across situations like that but the point of having a babysitter there is to deal with emergencies, otherwise there wouldn't be any point in having anyone there at all.
Accidents happen, it's part of life. It's perfectly true that we can't avoid all risk. But it's also the responsibility of the parents to ensure that if something does happen their children are with someone who can cope with whatever arises.
And power cut? Under current conditions really not extreme at all....
Now, if a 15 year old has done a 1st aid course they'll be able to deal with a choking child (providing they're mature enough to keep their head), a mature 15 year old would also know that in the case of a house fire you get out and call 999 and (crucially) be able to act upon that. Finally if they have instructions there's no reason why they shouldn't be able to deal with a power cut but being alone in the dark and resonsible for children is scary enough as an adult, so I would want to be certain that a 15year old could cope.
But then I appreciate that experience has taught me to anticipate the worst case and pre-emptively deal with it so red books are always left somewhere accessible, I know where the stopcock and fuse box is in every house I babysit in, ditto candles and matches (I also have a torch on my keyring), and one of the first things I do is make a fire escape/contingency plan covering a fire in the kitchen, a fire in the parent's room (from hair straightners being left on) and a fire preventing us exiting the house via the stairs.
Extreme, yes, but the job is to ensure the safety of the children in ALL circumstances.