Sadly, I doubt 3-day take-home assignments have much future as a means of assessment in the age of LLMs.

Might be true, idk? For all we know that professor now gives a 2.5-day take home assignments where they are allowed to use LLMs, and then assess them in an 1 hour oral exam where they need to explain approach, results and how they ensure that their results are accurate?

I don't think the 3-day take home is the key. It's supporting educators to have the intention, agency and capacity to improvise assessment.