I would bet that lots of very smart people have looked at the problem and thought it was viable if they’re moving forward. Also, the people in Iceland are very adept at geothermal (but maybe not this type).
I mean we thought oil the same way until we developed fracking. While it's not likely a 1:1 relationship with fracking, I'm sure some clever geologists/drilling experts could massively increase the surface area available for heating given the right incentives.
As for facilities, the volcano eruption rate is rather low on human timescales, especially for effusive eruptions that don't tend to blow the entire area to bits. Getting 50-100 years between eruptions that could possibly total the facility is likely worth it as you don't have a direct fuel cost.
But this is neither here nor there. The energy you extract from a geothermal well is heat, which then needs to be converted to electricity. The BTUs in a good oil or gas well exceed those of a geothermal well. You have the same issues of the well becoming less productive. The remediation strategies for this are similar, i.e. pumping fluid back into the ground.
I can't speak to the receding magma or facilities damage, but "proportional to the cross-section of the borehole" is just like first year thermodynamics. If someone has more familiarity with electricity (I guess common on HN?), here's a reasonable introduction to the comparison to circuitry: https://lpsa.swarthmore.edu/Systems/Thermal/SysThermalElem.h...
To me, it seems like the magma would could enough/create enough friction in a small borehole to prevent catastrophic failure. However, that’s just a feeling & I’d love to read more about this.