many people in New Zealand ... are saving large on the electricity bill by paying spot rates for power
How many is "many"? I suspect it's actually a few people who can organise their lives around power prices and that the sort of low-income people who really need this kind of thing cannot be that organised. Very simple things like not heating your home during the day aren't always practical if you aren't out at work, and running the washing machine during the cheapest period could save a lot of money, so long as your wash cycle doesn't take three hours and you don't have the sort of family that means you have to run the thing at least twice a day.
And then there's the extremely obvious point that has been missed by practically everyone (apologies if this has already been mentioned further down) that the energy companies are not in the business of making losses. If a large enough number of people reduce their bills, the companies will simply have to put the price up across the board in order to maintain profitability.
Yes, it can work, but only if the numbers taking up the opportunity are low, and everyone else pays for them.