I'm a geologist who has worked a little in Enhanced Geothermal Systems and (independently) in volcanology though I am a specialist in neither (I mostly work on earthquakes, and probabilistic seismic hazard analysis). I think this paper is quite interesting but the caveats are briefly noted though actually enormous.

A key one is here: Beyond human intervention, huge pulses of heat energy into the magma chamber may at times precipitate eruptions, with brief periods where the heat flux is so large that engineering solutions would be impractical. If heat flow were sufficiently massive then it may be impossible to mitigate supervolcanic eruptions.

From what we know about more well-studied volcanic systems (which are volcanic arc systems like the Cascades in the US or Mount Fuji in Japan), the heat flux into the upper magma chambers comes in the form of episodic injections of extremely hot basalt from the deeper magma plumbing systems (5-20? km depth). The size of these injections likely scales with the size of the volcanic system, so for a mantle plume they may be enormous. The heat flux is not steady state and the shallow crust/ upper magma chamber does not just heat up linearly with time until the eruption threshold is reached. We definitely have no control over the deep basalt plumbing systems and can't drill anywhere near that deep and hot (Deepwater Horizon, which by most metrics is the deepest well drilled, reached 12 km depth in cold crust, not getting above 120 deg C [1], but in the Yellowstone area this would be almost certainly well above 500 C (perhaps 900-1100 C)...

Additionally the failure mode for hydrothermal cooling of the volcano is really bad. Explosive eruptions are basically triggered by the release of volatiles in magmatic systems (expanding gases in a magma froth as H20 and C02 come out of solution). As is stated a few times, the increase in temperature with depth above the magma chamber basically follows the increase in boiling point of water, so the system is essentially on a critical threshold. Perturbations to this can be quite bad because any volatilization of fluids in the system can cause a small phreatic (partially hydrothermal) eruption that could remove some shallow mass, which decreases the confining pressure at deeper depths and causes further volatilization due to decompression, leading to a runaway cascade of larger and larger eruptions culminating in a major magma-chamber-emptying eruption.

They mention this here: in any realistic system there is a possibility that, as we artificially extract heat energy out of the magma chamber, we could cause phase changes (e.g. volatiles coming out of solution) that would reduce the overall density causing expansion and cracking in the overburden, possibly opening a channel to the surface and precipitating an eruption.

Now also consider that n=3 over 2.1 million years. If this is a Poisson process, then the probability of an eruption in any given year is ~1.4e-6, or 1 in 1.4 million. Though the most recent 3 events are quasiperiodic (mean 0.7 M years apart, stdev 0.075 M years), before these 3 eruptions, the eruptive center was in a different spot farther to the southwest, and there was a 2.3 M year quiescence between events[2]. I don't think there is any clarity over whether the next major eruption would occur in the same magma chamber as the previous several events or would form to the northeast towards Red Lodge, MT. So even in a periodic, geographically stationary system, which is sort of the most dangerous scenario, we could say that we're 90% of the way to the next eruption which therefore has an annual chance of happening of 1 in 140,000.

I think that any sort of mitigation efforts are still going to try to address a rather low probability event with uncertain technology, possibly in the wrong geographical location, and could trigger the event we are trying to forestall. At a certain cost of billions (pocket change w/r/t the costs of an eruption, sure), and the major modification of the first and probably most famous National Park (and therefore the permanent slandering of otherwise promising geothermal technology in the eyes of environmentalists). Not sure what the value proposition of all of this is but maybe our efforts could be spent elsewhere...

[1]: https://www.nature.com/articles/s41598-019-42496-0
[2]: https://www.usgs.gov/volcanoes/yellowstone/summary-eruption-...