That's great, but unless society can get used to having electricity only when the sun is shining, we require at least one of three things (or a combination of them):
- Ultra long-range power transmission lines with low enough loss as to be economical, so we can transmit power from an illuminated part of the earth to a part currently experiencing night time (or very thick cloud cover, which is pretty close to the same thing). These, of course, will require large investments in infrastructure for power transmission across continents in extremely large quantities, and I'm not sure we have the technology to do so without losing the majority of the energy during transit. What kind of voltage would you need to, say, transmit power from New York to London while keeping at least 66% of it on the receiving end? Not to mention the political and economic complexities of managing this, and the security risks as well. We'd need backup plants (probably of a more traditional variety) ready to fire up at a moment's notice if something were to happen to the supply coming from another country.
- Enormous amounts of energy storage. This is currently a major issue for us. Batteries are expensive, and all the *good* batteries actually DO require a tremendous amount of rare materials like platinum. Supercapacitors have been talked about as a potential replacement for batteries for a very long time, but no one has been able to get all the desirable characteristics into one device (low cost / easy to manufacture, high energy density, minimal loss over a storage time of at least 12 hours, and large number of charge cycles before replacement).
- Other sources of power to cover the times when the local/regional solar output can't cover demand. If those other sources end up not being wind or hydro or geothermal (due to geological or meteorological conditions), it's probably going to be nuclear fission (nasty waste) or fossil fuels (doesn't solve the problem we're trying to solve). Having to run nuclear 50% of the time means you may as well run it 100% of the time, because of the high cost and time investment required to start up a nuclear plant. Fossil fuel plants are more flexible, so we could actually cut our fossil fuel use by 50% using this scheme, but that still leaves the other 50% on the table, which isn't so great and sends the wrong message.
An effective system would probably use a combination of all three of these measures to try and deal with the many logistical problems of solar, but the unfortunate fact is that we're very deficient on the materials science, manufacturing technology, political will, and raw materials that would be required to comprehensively cover up solar's limitations by strategically employing all three of these methods.
Without being able to solve these problems at a national and eventually global level, you will end up with an extremely inefficient system, and the inefficiencies in it will cause a "death by a thousand cuts" type problem, where your resulting solution provides intermittent blackouts to most customers (or alternatively, no blackouts but a large percentage of the time running off of other energy sources); costs way more than their old fossil-based power; and requires a significant amount of traditional power plants to still run to cover up for the worst of its problems.
Oh, and you also seem to have based your math on the assumption that per capita power demands won't increase. Unfortunately, in order to comprehensively eliminate fossil fuels, we'd need to convert the vehicle fleet to EV (or at least plugin hybrid), which means per capita electricity demands are going to skyrocket.
At the very least, we're going to need even more nuclear power plants to provide a strong base load in the future. Solar might enable us to shut down numerous coal power plants at least some of the time, but you'd have to over-engineer your effort to satisfy the world's energy demands by a factor of eight or ten in order to compensate for: increasing demand per capita, increasing number of people, efficiency losses due to transmission distance, efficiency losses due to storage, and relatively unpredictable loss of production due to weather phenomena and the constantly-shifting day/night cycle. Some places that spend a lot of time with small amounts of daylight would have to be completely dependent upon external suppliers of energy, or else produce their own energy using traditional methods.
Take into account all of that, plus the fact that we are not currently producing photovoltaic cells at a rate that is exceeding the current increase in power consumption year over year , and it seems that we would have to embark upon a worldwide project the scale of which has never been attempted before, in order to do this.
And politically, most people just *aren't willing* to sink that type of investment into a system, even if it's ultimately for our own good.
To wrap it up:
1. Rare earths play a significant role in the *total solution* for solar, particularly where energy storage is concerned.
2. No one is willing to bankroll a project large enough to make solar the simple majority energy source of humanity (50.00001%), let alone anything more than that.
3. Making solar cheap and efficient would require significant advances in science and engineering that may not be reachable for another couple of decades at the earliest.
4. Unless we keep *most* (if not all) of our existing power production facilities operational and fueled and ready to come online, I don't see us having the means to solve the day/night reliability problem of solar (the energy storage demands are just too great). And keeping the old guard around will be extremely costly and unprofitable if they aren't operational 24/7.