Some things are valuable, because they keep people alive and healthy in the short term. Some are valueble, because some people find them inherently valuable. Pure mathematics is in that category. And then there is bureaucracy.
Bureaucracy has no direct value, but it may have indirect value, if it helps us achieve things that are more directly useful. Pure mathematics has had a lot of indirect value until now. It turns out that training people to do mathematics for the sake of doing mathematics, at any level from schoolkid to mathematics professor, teaches skills that transfer to other domains. If human thinking becomes obsolete, that indirect value may be gone, but the direct value will remain.
The results in pure mathematics are largely irrelevant, except as means of acquiring transferable skills. Sometimes they have practical implications, but such situations are exceptional. And there is not much correlation between the practical value of a result and its value as seen by mathematicians.
See we're taking about inherent value but part of that is my valuing a not nonsensical explanation. And saying math has intrinsic value because some of us treat it as that is nonsensical and anti-science or anti philosophy. It is not based on an intelligible definition of value. Which goes to my original point that when people trot out these arguments they are really thinking carefully about what they are saying. And the more you see these talking points repeated I have to ask who is putting forth these notions. And so every time it is someone making these sweeping declarations about "value" and other people are supposed to accept that. It is a kind of ideological being talked-down to, what gave them the position to declare the ontology of value and so forth. And that is pattern once pointed out you'll see people keep doing it.