I mean, I agree variable rates could stop people running clothes dryers, close down industrial users and so on. But the remaining demand would be extremely price-inelastic; How much would you pay to stop your pipes bursting? $3000? $10,000? More?
So long as the amount of power being generated is less than the amount of power needed to prevent anyone's pipes freezing someone's pipes are going to freeze, and no amount of shuffling around who gets the power is going to change that fact.
That said, I think the higher order effects of a market regulated to require more responsive rates could lower this threshold.
For instance, if every homeowner in texas might get stuck with an expensive winter heating bill because of new regulations around rates, we would consider requiring all new construction use gas furnaces where possible.
As it currently stands, I was just talking to a friend who got taken to the cleaners because his brand new construction uses resistive/heat pump for heating, despite the trivial & cheap availability of natural gas.
If rates are predictable enough that a gas furnace is sure to pay for itself over the next 10 years, people will easily identify it as a good investment.
On the other hand, if the rates are variable, switching to gas is a gamble. Might save me loads of money, might not save a dime.
The thing I am concerned about is masking market forces from consumers. Potential "band-aid" solutions for the current approach might include adding a capacity market, or requiring that all consumers operate on a variable rate plan in order to more fairly mediate demand vs supply. Customers with fixed rate plans in Texas had no incentive to not run things like electric clothes dryers or resistive pool heaters while others were literally freezing to death.
If you think about fundamentals of consumer behavior and markets, a fixed rate electric plan is like buying an insurance policy or options contract on some underlying security. If you have a lot of derivatives in play, bad things almost always happen regardless of the underlying asset types.