Yes, I expect practitioners to care about something useful, assuming the result has been properly written up and explained in a way they can understand. Scientists want good results and will adopt new tools if you can make a case that they will help them publish impactful papers.
Again, it's pretty telling specific applications aren't mentioned, and instead there's just vague gesturing. How can we expect scientists to "do the field work" necessary to bring the applications to fruition if we can't even tell them what those applications are?
Also, regarding your first sentence, the vast majority of influential mathematics was indeed "immediately acknowledged," because it made progress on some important problem. Perfectoid spaces are a recent example.
Again, it's pretty telling specific applications aren't mentioned, and instead there's just vague gesturing. How can we expect scientists to "do the field work" necessary to bring the applications to fruition if we can't even tell them what those applications are?
Also, regarding your first sentence, the vast majority of influential mathematics was indeed "immediately acknowledged," because it made progress on some important problem. Perfectoid spaces are a recent example.