Price performance. If the failure mode is slow, then my sport (rowing) could love this for cheaper boat construction which is stronger than fibreglass but cheaper than carbon fibre. I imagine surfboards and kayaks could work too.

Being flexible and non conducting is useful.

In addition to what sibling posts say, basalt is certainly abundant. Per Wikipedia, 90% of volcanic rock on earth is basalt. We're not going to run out of it.

I can imagine (I have no clue about this, I just watch manufacturing videos) that this is easier to mass produce. A less refined version of this is used to make Rockwool, an insulation material similar to fiber glass. Melt the stuff, extrude it, ????, profit. https://www.youtube.com/watch?v=t6FWPTZjwLo

See uses here: https://en.wikipedia.org/wiki/Basalt_fiber I am no material scientist, so cannot comment on actual facts why it might be better in specific cases than Kevlar, Dyneema or Carbon. But from experience there's a lot I don't know and especially in engineering there's a lot to consider when putting materials under stressful conditions that might put this in in a specific spot superior to those mentioned above.

Each material has its own issues. Kevlar is very difficult to work with (need special scissors to cut and you can't sand the finished product), Dyneema is sensitive to UV degradation. Carbon is $$$. Basalt sounds like the sweet spot for some of my applications but afaict it can't be purchased by the yard like most materials so is essentially unobtainium to a hobbyist who can't afford a $1k or so roll of material.

All those burn.

Basalt does not burn, so its main competition is glass fiber, not organic fibers.

Also, those 3 mentioned by you are currently quite expensive in comparison with other fibers.

I suppose because basalt cannot be patented. Or at least cannot be patented outside the US.

Say, is Carbon in your statement a trademark?

It seems to be more heat resistant?

"I don't see why" has never been the bar for scientific advancement, fortunately. "Someone is curious" is sufficient, and "Someone involved sees potential" provides funding.

Seriously, how much else of the world's technology would you summarily do away with, because you simply don't see the point?