I do believe that volcano monitoring is very much a legitimate
function of government. Furthermore, like Richard Posner, I think
we do not spend enough time and energy worrying about extreme
disasters, including volcanos and also problems from
Yellowstone National Park. That said, I would like to point out that, from what the web indicates, the private sector started doing volcano monitoring before the public sector did:
Perhaps “modern” volcanology began in 1912, when Thomas A. Jaggar, Head
of the Geology Department of the Massachusetts Institute of Technology,
founded the Hawaiian Volcano Observatory (HVO), located on the rim of
Kilauea’s caldera. Initially supported by an association of Honolulu
businessmen, HVO began to conduct systematic and continuous monitoring
of seismic activity preceding, accompanying, and following eruptions,
as well as a wide variety of other geological, geophysical, and
geochemical observations and investigations.
A lot of cutting edge volcano monitoring is done at universities; many of them are public universities but they are not acting in their public capacity. They may be receiving public sector grant money. Here are blogs about the history of volcanology. Here is a good essay on contemporary volcano monitoring. Here is a catalog of all the current methods used. Here is how GPS is used to monitor ground deformations. Interoferometric synthetic aperture radar has become very important.
It is possible that some animals are better volcano monitors than we are, but I do not blame the public sector for this differential.