I would certainly agree that a store of alkaline cells is prudent in case of power failure, in this case the probem was only in the OPs home and batteries could be readily purchased. in the event of a general blackout it is probable that the store would either close or run out.

As regards the cause of the problem, in addition to installing smoke detectors in the recomended places in your home, I would suggest an additional smoke detector close above the electrical panel, this could give valuable early warning of any overheating.

In the UK the use of RCDs is to be recomended, in the USA these are known as GFCIs and are already in widespread use.
Such devices protect against leakage of current to earth/ground which can kill or start fires, they do not in general protect against overheating caused by loose connections or overloading.