I've seen articles covering semantics-related topics that present a formalism where every finite verb receives an event argument. This comment on a question on this site briefly describes what an event argument is.
I think you might be able to use this event machinery to explain why finite verbs in various sentences receive perfective or imperfective aspect. The idea being that the perfective introduces a new event and the imperfective does not. This isn't my idea. I'm cobbling together some half-remembered ideas presented in a few papers I read a long time ago, I'll try to find a source. I suspect the real distinction is more complicated ... and the choice of aspectual marking depends on more than whether the event in question is a new discourse participant or not.
That being said, I wonder if there's a language with an aspect distinction that's close-to-ideal from the perspective of events and could be used to support a theory of events as verb arguments in the first place.
I'm wondering if there are any languages with a 2-way aspectual distinction that aligns particularly well with the "am I introducing a new event?" test.