Why do many philosophers seem to have accepted without argument that experience can only give us epistemic access to how things are, not to how things must be or how they could be? As far as I can tell, Plato, Kant and Hume were all convinced of the truth of (some version of) this claim, and it also has later advocates (I can think of relevant passages in Whewell and Chisholm).
But even if we thought that all modal truths were knowable a priori (and we had not yet appreciated that a priori knowledge may be empirically grounded), what would be the grounds for denying that experience can provide some (a posteriori) form of epistemic access to modal truths?
Granted, we never see modalities or bump into them. But we never see or bump into quarks or dark matter or magnetic fields either. We (or rather, those experts to whom we delegate such things) infer to their existence as the best explanation of what is observed. This is a perfectly respectable way for experience to provide epistemic access to some swathe of reality.
Is it perhaps assumed that modal truths cannot serve as explanations of the things we observe? Or is it that some other, non-modal explanation will always be better?
Alternatively, is the assumption that experience cannot provide us with epistemic access to modal truths just outdated? Has our epistemology moved on, with the realization that we can have empirical grounding for believing in something without actually bumping into it, and left this old-fashioned assumption behind?