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...>
Secondly, there exist efficiencies of scale that come with drilling at ten or a hundred sites rather than just one or a few.