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.)
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.