What are ways in which limestone caves are useful?

One in Ohio, as i recall reading in Popular Mechanics years back ( sixdties or seventies) was converted into a huge, underground Mushroom farm, originally it was a man-developed Limestone mine . so there are applications to general commerce.

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Old limestone mines -or underground quarries as they are sometimes termed - are used for various purposes such as mushroom farms as you say, or forstores, as well as being visited in their abandoned state for their industrial-archaeology interest.

However the question is about caves, not mines. They are (present tense) in the way any landscape feature is useful, as a part of nature to be respected and admired, whether as show-caves or left unaltered for recreational caving and cave-studies.

A cave that is still "active", i.e. carrying its formative stream is useful as a part of the natural water-supply for its location, for it brings water from the hills to the spring that is its outlet.
A cave is also valuable as a wildlife habitat in various ways.