Love example 2. Maybe there is a name for this already, but you could generalize the semiotic fallacy to arguments where there is an appeal to any motivating idea (whether of a semiotic nature of not) that is exceptionally hard to evaluate from a consequentialist perspective.
Example: From my experience, among mathematicians (at least in theoretical computer science, though I’d guess it’s the same in other areas) who attempt to justify their work, most end up appealing to the idea of unforeseen connections/usage in the future.
If they appeal to unforeseen connections in the future, then at least one could plausibly reason consequentially for or against it. E.g., you could ask whether the results they discover will remain undiscovered if they don’t discover it? Or you could try to calculate what the probability is that a given paper has deep connections down the road by looking at the historical record; calculate the value of these connections; and then ask if the expected utility is really significantly increased by funding more work?
A semiotic-type fallacy occurs when they simply say that we do mathematics because it symbolizes human actualization.
(Sometimes they might say they do mathematics because it is intrinsically worthwhile. That is true. But then the relevant question is whether it is worth funding using public money.)