And for the telephone, that came when police and fire services were hooked to them, meaning you can call them in emergencies.
Yes, I'm sure calling them was first and foremost in Queen Vic's mind when she and Mr Bell were phoning around the countryside.
AFAIK, no Internet service operates in true life-or-death emergency capacity yet.
Actually many do these days. Did you not know that most phone traffic in many countries is carried over POTS only as far as the nearest link to an internet-based backbone? Calls between landlines are now routed over the net at least in most developed areas (rural areas and developing nations may differ). So your calls from your home to the local fire station will most likely go over IP for part of the trip if you live in any reasonably modern city.
If you call from a cell phone, it could be IP all the way. If your phone service is over fibre now, then it is IP from the box your household phone is plugged into, routed over the internet before it even leaves your home.