Why are precision and recall used in the F1 score, rather than precision and NPV?
F1 score weights precision and recall equally but there are easy generalizations to any case where you consider recall $\beta$ times more important than precision. See https://en.wikipedia.org/wiki/F1_score:

$F_\beta = (1 + \beta^2) \frac{precision \cdot recall}{\beta^2 precision + recall}$

F1 is just a harmonic mean. The simple mean doesn't quite make sense because precision and recall have the same numerators (true positive) but different denominators (test positive, condition positive). So only a harmonic mean makes sense. I don't know if there's more theory to it than that -- the simplest weighted mean that make sense.

I think I get the gist of your point, which I paraphrase to refer to the fact that precision has "test positive" in the denominator so is quite sensitive to how much the classifier marks positive. For this reason you don't so often see, for example, precision-recall curves. You see ROC curves which are recall-specificity curves (true positive rate vs false positive rate).

That's closer to what you suggest but you're suggesting PPV vs NPV. Sure that could be valid depending on your use case, but I think the argument tends to cut the other way, to recall-specificity instead, not precision-NPV.