...and highly impure sources; one thing they're going to have to do is to go through our waste dumps to recover materials they need.
One of our biggest waste dumps is the oceans.
There are three critical materials that are readily available from seawater; one is fresh water, obviously, the second is carbon in the form of carbon dioxide, biomass and plastic waste, and the third most important in my mind, is uranium.
It is possible I think to utilize reduced pressure distillation techniques, alluded to in the paper discussed in the OP, to purify water in an energy efficient manner, particularly by process intensification, that is by putting what is now considered "waste heat" to use. The intakes can be adjusted to recover uranium, although humanity will actually not really require uranium for centuries in a plutonium cycle. (There are, however, good reasons to recover uranium anyway from sources having NORM (naturally occurring radioactive materials) and mine tailings and the like.)
Other elements that you mention, for example gold, may be recoverable depending on price and demand. The price wasn't high enough in 1919 when Fritz Haber tried to do this to "save" Germany.
If we are going to utilize biomass, plastic waste, and the various forms of carbonates in the oceans, this is going to require supercritical temperatures, which is very different than anything we're doing now. I consider that supercritical fluid technology will be an absolutely essential technology if we have any hope of sustaining the future, not just supercritical water, but supercritical carbon dioxide, and other supercritical materials like current day curiosities like DME.
The recovery of elements from mining tailings, waste dumps (including the atmosphere and the oceans), will require the overcoming of the entropy all previous generations have left for subsequent generations. This of course will require huge amounts of energy.
The use of supercritical water would give a relatively clean way to desalinate and simultaneously concentrate the minerals in seawater. I expect that some of these recovered materials, particularly brine, will represent disposal problems in their own right. This is already a problem where desalination is widely used. I have never worked with TEOS-10; since I lack the time and quite honestly the computer skills to do so, and so I'm not sure whether the thermodynamic equations are validated to the supercritical regions and the resultant phase systems. It's possible that they have been, since supercritical seawater is discussed in some papers I've seen relating to oceanic volcanoes and other geothermal systems. I do hope that I can convince my son to consider these equations of state among others.
I will say this, at high temperatures such as those obtained in supercritical water, many processes are known for thermochemical waster (and carbon dioxide) splitting, and the production of hydrogen as a captive intermediate and not as a consumer fuel, as you say, is relatively straight forward from seawater. I also think that as a side product of seawater processing, excess electricity might be utilized, particularly where it required as "spinning reserve," the solid oxide fuel cell described in this paper seems quite attractive to me to produce hydrogen. I do believe these can be adapted to seawater, while conceding that current technologies do not cut it where seawater is concerned, as the authors of this "wind to hydrogen" scheme plainly confess.
There is really only one option to provide the energy required for all this, uranium, and to a lesser extent, thorium and/or deuterium and tritium if they ever actually make nuclear fusion work. One thing is clear is that nuclear fusion will not be available in any time frame to address the on going and worsening crisis.
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