I'm surprised a 12v based deep freezer that runs off a reasonably sized solar panel is not more popular/affordable. With the right amount of thermal mass, and good insulation, and a small battery you could greatly extend how long your food stays cold. There are a lot of people who live in places where snowy weather or high winds and loss of power is an eventuality. In an emergency losing your food is a bigger concern than just the cost of the food.
https://fridge0.branchable.com/
Or go a bit higher end and put a larger solar and battery instalation with an inverter that can power the whole house. As solar panels and lithium batteries come down in cost that's becoming increasingly attractive for rural areas where the grid is flaky the best of times.
But yeah cheapest thing to do is get a furnace transfer switch and a generator. That seems to be how rural people in the upper midwest avoid freezing to death when the power goes out in the winter.
Your basic point makes sense to me though of course thawing isn't even.
ADDED:
Doing the calculation. It takes 334 joules to melt 1g of water vs. about 4 joules to raise that same gram of liquid water 1 degree. Freezer temp is supposed to be about -18 degrees Celsius.
So the latent heat of melting is a bigger deal than a few degrees of raising liquid temperature. So you should have ice packs maybe somewhere in the -10 degree range which is what I assume commercial ice packs do.