I agree, and I think LLMs can potentially do a better job than more conventional methods, so long as they're provided with enough content.

Another aspect of context that could be relevant to your work may be how people are nested within households. In some record linkage scenarios you can run a linkage on household membership and use this to make person linkages more precise. I imagine an LLM agent could also use this information effectively if it were explicitly provided, but sometimes they miss logical leaps like this