The first is very lossy: HVDC is the most efficient way to transport bulk electricity, and it loses 3.5% per 1000km. You would need to transport electricity about half the way around the earth of the earth's circumference, or about 20,000km, meaning you would lose about 50% in transit. So this would depend on a drastically more efficient way of transporting power (superconducting power lines?).

The second is not possible with current battery technology.

And that still doesn't answer why this arrangement would be better than a nuclear (base load) + solar (daytime variable load) + natural gas (nighttime/cloudy conditions variable load) mix.

I just did a quick calculation in Wolfram Alpha and found that (assuming perfect efficiency), to store enough energy to power the United States for half a day would take 713km^3 of water raised 1km. That's about half the volume of Lake Ontario pumped up one kilometre during the day, and down again at night.

I guess that's theoretically possible but it would be a hell of a megaproject, and for what?

Imagine some one using an oil lamp in the pre-electricity era saying this. Would it even make any sense at all to replace a perfectly working oil lamp/candle with a light bulb at the expense of century worth mining of copper, putting down massive infrastructure, setting up dams for just glowing this small time bulb?

The widespread use of electricity or trains or airplanes or dams or any major paradigm changing invention in human history requires mega engineering projects for a very simple reason. You have to deliver at scale.

If one can go totally without fossil fuels chasing such projects makes all the sense in the world.

I disagree there. All the examples you stated developed gradually starting small and expanding. The first railways appeared in Europe in the 14th century and didn't really take off until the 18th century with the development of the steam engine.

Even air travel, which went from the first heavier-than-air flight to first commercial flight in a remarkably short period of time of about 27 years, piggybacked off of earlier lighter-than-air travel that had existed for centuries. In the Napoleonic Wars, balloons were used for surveilling the battle field, and airships appeared in the mid 19th century. People already knew that air travel was commercially viable and militarily useful. Heavier-than-air machines were a major improvement on the concept, not something entirely new.

This is a common theme in technology: a primitive form of the technology exists for a long period of time in niches. Then, after a period of time, there's a key invention -- the steam engine for rail travel, the dynamo for electricity, the airplane for air travel, the transistor for computers -- that causes the technology to explode in a short period of time.

That key invention is the last piece in the puzzle, not the first. The earlier developments prove the viability of the concept, build up the infrastructure to support it, and justify large investments in developing the key invention. But if you don't look at the history before the key invention, you'd think that computers and electric generators and railroads and aircraft appeared suddenly and had large amounts of capital suddenly invested in them.

And that brings us back to my original point: all those technologies had clear advantages over their predecessors. What advantage does an all-solar future have over a mix of sources? Simply getting rid of fossil fuels is not good enough.

It may be that aluminum electrorefineries and data centers simply have to be installed next to hydro plants instead of solar plants. And CNC machine tool plants will only operate when the sun is up. So be it.