The issue with the Hebrew (I mean Biblical Hebrew prose here) verbal system (HVS) is accounting for the different uses of qatal and yiqtol at the appropriate level of generalization. It's not that difficult to list all the different functions of these verbal forms, but finding a way to characterize the whole thing has proved controversial.
Everyone agrees at this point that the HVS is not a tense-only system. This can be demonstrated with one fact:
(1) If HVS were tense-only, then yiqtol could never receive a past interpretation. But it can receive a past interpretation in prose (with the past habitual use).There is much less unanimity that HVS is not an aspect-only system. In fact, my impression is that this view is held by the majority. Nevertheless, this approach also fails, for the following reason:
(2) If HVS were aspect-only (e.g., perfective/imperfective), then qatal could receive a future interpretation. But in fact, it does not receive a future interpretation in prose.Hence it seems that HVS is a combined tense-aspect system, with qatal being both past and perfective, and yiqtol being past imperfective (habitual), future (either perfective or imperfective), present (general, not actual) and modal. Many languages of the world combine tense and aspect (e.g., Greek and English) so there's nothing weird or unwelcome about this. Nevertheless, there is still a hankering (in me, at least) to find some feature of the qatal/yiqtol opposition that licenses its several interpretations without any appeal to the arbitrary.
To me the most important clue lies in an argument made by Jan Joosten (in this JANES article), that yiqtol never indicates the actual present (similar to English present progressive), only the general present (gnomic or habitual). I find Joosten's argument convincing, although you can still find statements in the grammars to the effect that yiqtol can function to indicate the actual present. If Joosten is right, then there are not any functions of yiqtol where it refers to an actual, instantiated verbal action (event, state, or process); that is, it is non-referential in that there is no particular action that it picks out.
Here, then, I think is the opposition. Qatal is referential, yiqtol non-referential; again, by referential, I mean that it points to or picks out a particular instantiated action. If qatal is referential, then that entails past tense. The entailments of yiqtol are not as constrained as those of qatal; not having referentiality means that it can be used for a typical action in the past (habitual) or the present (general present) or for a non-instantiated action (such as the future or modal). Hence the wider range of interpretations or readings (in the semantic sense) that are available for yiqtol.
"Referentiality" is usually discussed in terms of nouns and noun phrases, and verbs are not considered in that context. Nevertheless, I think one can argue that verbs can be referential (like a definite noun phrase) or non-referential (like an adjective or an indefinite noun phrase).
This doesn't explain the workings of what I call the "secondary" HVS, that of wayyiqtol and we-qatal. I'll discuss those at a later time. Also it leaves open the use of qatal and yiqtol in poetry, where some possible counter-examples to (1) and (2) above can be found. I don't believe that they are true "defeaters" of my proposal, because quite often, in my view, what seem to qatal and yiqtol in poetry are actually forms of we-qatal and wayyiqtol that vary because of the peculiar modes of coordination (and conjunction reduction) available in Hebrew poetry. Again, I'll leave that for another time. Suffice it to say that in the final analysis I think the HVS is ultimately uniform in prose and poetry.