(They've already stated they won't do Portal: VR because of the nausea issue.)
I completely agree with your analysis, they would need to completely switch up the ambitions from a writing perspective for Portal 3 to make any sense. There are plenty of super interesting stories to be told in Aperture Labs, but I don't think that Valve is structured to write any of them
Valve has always been "gameplay/tech first, story second", and it just happened that Portal 2 delivered unexpectedly well on the writing. But I don't think they can make a game with gameplay/tech twice as ambitious as Portal 2, and at the same time double down on Portal 2's amazing writing. They're just human and most of the people involved have moved on with their lives; in fact Portal 2 was their last truly ambitious narrative-heavy game, and they had to hire the old writers as consultants to make Alyx (which I haven't played but from what I heard the narrative wasn't on HL2's level).
I'd love to be proved wrong but IMO there won't be a Portal 3 for as long as Valve exists in its current form.