I've already offered my suggestion: do it the way every other game does it and have the companion characters speak their lines without player input, when appropriate.
Well, the problem with that solution is that it would require the devs to treat SP and MP very differently. That's imo completely out of question (time, budget, etc). There must be a system that could be used with only little adaptions for both SP and MP. In coop your companions are controlled by other human players so there can't be any automatically initiated companion interactions in dialogue. Something like that doesn't exist yet. There is no "narrative AI" since the game sees companions as possible player characters that could anytime be controlled by humans. The devs would have to create such scripted multi-character dialogues from the scratch and with only SP in mind (since they wouldn't happen in coop MP in the very same situation). That's something that just won't happen, I'm afraid.
The issue with DOS2 is (like it was with DOS1) that it's primarily made with coop/MP in mind in every possible situation. Every solution for SP must either basically just be the same or at least be something that doesn't require a completely different system or design approach.