Let's imagine a language that has developed out of a formerly inverse alignment language or an obviative-proximative language into something more "average". Now, we also know that "and" tends to have a temporal ordering effect when coordinating VPs, i.e. an utterance like "he stopped and got out of the car", we parse this as his stopping first and getting out of the car later, even for verb-pairs that aren't necessarily as clearly temporarily ordered. We also like to think there's a kind of causal link unless we have good extralinguistic knowledge to imply there shouldn't be one.
Anyways, now imagine that the direct marker or proximative marker is generalized and a case system starts distinguishing subjects and objects. However, the obviative congruence marker (or the inverse marker) survives in one context and one construction - originally, following a conjunction, it had a causative meaning, i.e.
Subject Verb1-DIRECT Object-ACC and Verb2-INVERSE
Subject Verb1ed the Object and made it Verb2
Over time, the requirement for a Verb1 to be present weakened:
Subject and Verb2-INVERSE Object
Subject made Object Verb2
Of course, now 'INVERSE' (or obviative) no longer signifies INVERSE (or ...), but rather 'causative'.
"And" as a grammaticalized thing is known from Hebrew, but there it has somewhat different use. This could of course be very fun if, in addition, and and with were conflated in the language.