Yes in a scenario, which you are in a cold climate which it is always cold outside. Then yes, thermal energy storage would be an extremely efficient option.
It doesn't apply to most living humans but I grant you that special case.
yes, I did look at your link and noted all of sites are those near mountain ranges; which I certainly grant you is near (within 100 miles of) most human population centers.
There are a great many "promising" technologies in the pipeline, the real question is which of them actually suit our needs and only via real world trials will we discover the flaws and see if the benefits outweigh the flaws.
well no storage can be 100% efficient but you are correct that thermal storage is very efficient if you want a thermal gradient to leverage for heating (cooling as well)
I am assuming you mean Pumped-storage hydroelectricity when you say PHES and no it also falls under F=ma, but when using the terrain is able to increase the amount of mass to a more industrial useful scale. The larger the scale the smaller the losses. Hence most economical when one has mountains for the storage of the water. (metal/plastic tanks on elevated platforms tend to be much less efficient and more expensive).
I guess it depends on what you mean by rare long duration events but yes one can imagine a situation where the burning of hydrogen is justified on an energy needs basis.
Depends on what you mean by a huge problem.
If you are referring to energy loses due to the large distances and the electrical resistance of the wires carrying that power; you'll discover those loses are directed related to current and that you can trade current for voltage and trade voltage for current; so we can avoid losses by upping the voltage.
If you are referring to the fact that the Earth's crust is moving, we can have geologists do some work; estimate the distances spaces where we will be running our wires and put in sufficient slack to cover the time period until the next maintenance window.
If you are referring to weather event induced disruptions in the grid (wind/tornadoes/etc taking out power lines) then you build alternate paths to route around damage.
If you are referring to solar storms and coronal mass ejections, then you need standards in your equipment to deal with out of spec distribution lines.
All of which are technical problems and easy to solve.
If you are referring to the bureaucratic hellscape that is international coordination and cooperation, then yes that is the only huge problem preventing such a solution, despite its numerous global economic and environmental advantages.
storage is only a problem if the global distribution grid is not created. The sun is always shining somewhere, especially if you realize we can leverage space to extend our collection.
cranes are just stupid energy storage (the F=ma bit basically makes this a non-starter) . Water in pumped storage only works out in huge scale (where you have mountains to provide a massive storage pool).
compressed air storage misses the point, use just a little more energy and you can use that energy to thermally separate CO2 from air. (This is a productive use of energy but bad efficiency for storage)
hydrogen production from water is a productive use if we want to remove hydrocarbons from some chemical processes but it is not an efficient battery.
Thermal storage of energy is very inefficient and not a good idea unless you are willing to waste a good deal of available energy.
And flywheels are not even mentioned and very wrong information about Tesla power walls.
Efficient is sexy
The breeder part is the production of U-233 (which is then fissioned and used to provide the neutrons for converting Th-232 into U-233 (with a chemical separation and decay storage step in between)) which although has a tight neutron economy is viable.
Working reactors for such designs were funded by the US airforce and they did operate as expected.
If you wish to argue that one will need U-235 as a startup fuel or that there are technical problems in large scale energy production it is not yet able to address, I would definitely agree on that; the technology needs more research before we depend upon it and that Uranium light water reactors are likely to be the running standard until such time and needed investment occurs. But we have enough U-235 in nuclear waste stockpiles to fuel our civilization for a thousand years to work out the details.
you don't need U-235 for nuclear power. In fact a Liquid Thorium-Fluoride thermal breeder reactor would be a more industrially useful nuclear design and Th-232 is available to power our civilization for a billion years (assuming no growth in energy consumption)
Short version:
No, but we probably can feed more people if we eat less meat.
Well going renewable is a political question not a technical one.
We are not doomed by nature but by the things we love.
in software these days it is: good, cheap or fast; pick one (if you are lucky [usually things are just bad, expensive and slow as f&*k])
heating is not done year around (365.25 days/year) for the majority of the world's population.
Hence why places which need heating year around are generally considered an edge case.