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.
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.
---
Water (liquid) - 4.80 J/g.K
Water (solid) - 2.108 J/g.K (transition 334 J/g)
Brine (liquid, 300g/L) - 2.48 J/g.K
---
So 1 gram of water (s) going from -18C to 0C (liquid) is 373 J.
1 gram of brine (l) going from -18C to 0C is 44.64 J.
Seems like ice is a better choice? The phase transition requires a huge amount of energy.
Brine is 70% more dense than water, so if you do it by volume, one mL of brine would be 76 J, so better, but still only ~1/5 that of pure water.
Why are you excluding the phase transition energy of the brine? Presumably you can calibrate the salinity so it freezes at around say... -15C, and set your freezer to -18C. That way it's absorbing heat more heat when it's colder, which is helpful if you want to keep your food frozen. The latent heat of water isn't of use to you if all your meat is already thawed.
Or you can have normal water which is frozen at -1c and liquid at 1c. Your pick.
The handy thing about the brine is that its absorbs heat at a temperature below that which everything else thaws. So as the brine thaws it keeps your freezer at -18c which means everything in it is still frozen.
I mentioned -18C because that is the recommended minimum temperature for freezers such that some foods can last almost indefinitely; certain chemical reactions are completely shut down.
Why don’t they do this with the ice blocks you get for keeping food cold on camping trips?
Adding salt to water reduces the latent heat density too (pure water is hard to beat there), but not as much as adding alcohol does.
You can do this by adding some salt-water bottles, which have a lower melting point, and will therefore absorb a lot of heat (heat of fusion) well below 0C. Eg add 250g salt/liter gives melting point of -18C.
Of course you waste some space on useless salt water vs potable - maybe there are better alternatives, eg fruit juice? Milk? Honey?