Secondly, the mining stations will be limited. Yellowstone is a vast land. There is expected to be no diminishing of the forest.
It is that we start at the periphery, very gradually going inward over a thousand year period. We should have enough data of the effects of our peripheral perturbations in the first few hundred years. It should provide a testable model for how to proceed safely as we go inward.
In other words, such a thing is completely infeasible given our current understanding of science and technology.
The time required to develop such a capability would span so many lifetimes that is it effectively science fiction.
I quite often think how people should be encouraged more to go to the natl. parks, they really take your breath away and are something to cherish. Buffalo running wild, Grey wolves if you're lucky, crazy weird geysers, go!
Via a flagged comment, a counterargument is deep geothermal, accessed via boreholes, and not strictly limited to extant surface geothermal fields:
Thomas Homer-Dixon is also an advocate that I'm aware of: <https://homerdixon.com/a-big-bet-on-geothermal-could-help-pr...>
I'm not sold on this (deep geothermal pilots such as the Geothermal Habanero project in Australia have proved expensive busts, and the productive lifespan of a given borehole is limited to a few decades). But it's worth consideration.
I've written on Habanero previously. The project consistently overran time and cost estimates, and delivered far less power than initially planned. That's not to say that the concept is fatally flawed, but it's also not the panacea first projected. By contrast, surface geothermal fields have been and are developed at commercial scale worldwide, and have been for years: The Geysers in California, in Iceland, Japan, the Philippines, New Zealand, and elsewhere. In fact most viable fields have already been tapped, with the largely untapped resources now existing in the African Rift Valley (largely within Kenya, where it could hugely bolster the country's fairly anemic generating capacity), and of course Yellowstone in the US, where there are significant environmental and political barriers. A USGS survey getting on two decades ago of US geothermal resources conspicuously excludes Yellowstone from any consideration at all. From 2007: <https://www.usgs.gov/publications/usgs-national-geothermal-r...>
See:
"Habanero Geothermal Project Field Development Plan". A largely sober summary of the project, noting that it's been concluded rather than expanded. <https://arena.gov.au/knowledge-bank/habanero-geothermal-proj...>
My own 2014 summary: <https://web.archive.org/web/20230601073717/https://old.reddi...>
Secondly, there exist efficiencies of scale that come with drilling at ten or a hundred sites rather than just one or a few.
Geothermal in Yellowstone is no better or more useful than geothermal at many other less important places. It isn't even the place with the most surface level geothermal energy in the first place. Overall geothermal technology advancement makes a lot of sense but starting said advancement via sandbagging for an outcome 1000 years after developing one of the best national parks to do so does not make sense.
Regardless of all of that, there are significantly more than the two possibilities of either starting drilling today or having catastrophe in an eruption.
Regarding the investment, if a 5 km well is dug, I don't expect it to exhaust its energy without a significant payback.
Geological diagram of Old Faithful: <https://public-media.smithsonianmag.com/filer/bd/06/bd0603df...>
From this Smithsonian article: <https://www.smithsonianmag.com/smart-news/seeing-beneath-old...>
"Old Faithful's Geological Heart Revealed": <https://www.sciencedaily.com/releases/2017/10/171005190243.h...>
Mostly addresses seismic activity, though there's some discussion of inferred structures from that. Based on the journal article by Sin-Mei Wu, Kevin M. Ward, Jamie Farrell, Fan-Chi Lin, Marianne Karplus, Robert B. Smith. "Anatomy of Old Faithful from subsurface seismic imaging of the Yellowstone Upper Geyser Basin". Geophysical Research Letters, 2017; DOI: 10.1002/2017GL075255 <http://dx.doi.org/10.1002/2017GL075255>
(The Smithsonian piece is based on the same article.)
Yellowstone has accessible thermal gradients. Even if a remote approach is made, say, outside the National Park boundaries and intended to minimise surface impacts, necessary drilling should be minimal, and a small number of wells should provide far more energy return than a large number of deep boreholes.
That said, I'm, ahem, well out of my depth here ;-)
The ability to achieve a high, long-term return on relatively shallow drilling operations probably trumps any learning-curve efficiency improvements in drilling itself. Sites such as Yellowstone (based on some former research I'd made) contribute significantly to US baseload electrical generation, should the US choose to exploit them.
It's also worth noting that there already is considerable expertise in drilling generally, with over 160 years of experience over millions of individual wells, and that the efficiency / improvement curve is likely fairly ... well ... exploited.
"Geothermal Drilling Costs" (2006) <https://www.thedriller.com/articles/84584-geothermal-drillin...>
"Cost analysis of oil, gas, and geothermal well drilling" (2014) <https://www.sciencedirect.com/science/article/pii/S092041051...>