The chats from AI dates would provide more transparency than today's algorithmic matching.

Do you have data, or a theory, about why they would produce more statistically valid estimates of people's romantic compatibility than prior algorithmic matching methods?

I agree that they do better on explainability issues in the sense that people could read the transcripts and say "oh yeah, I would/wouldn't have liked/enjoyed that", which they can't do if the OKCupid algorithm says they're a 92% match with someone or something. But how do we know that chatbots can be made a realistic enough simulation of a person to give relevant (indeed, more relevant) guesses about romantic potential compared to older matching methods?

Remember that existing LLMs have a whole lot of training that's not based on specific individuals at all, so to start with you have some component of "to what extent do chatbots that are told to simulate a conversation in a date end up acting like they liked other conversation partners?" with potentially a smaller component of distinctiveness of an individual.

(Another issue is that chatbots wouldn't know private or personal information that hadn't been revealed in training data but that might conceivably come up, if relevant, during a real date!)

Transparency into what, though? The transcripts would give you transparency into what the bots said, but not transparency into the people.

Comparing to other algorithmic matching isn't that useful, because it's all terrible. But I don't see how this method would be an improvement.

What exactly do you mean by this? In particular, how does the lack of transparency manifest in today's matching and how would the chat content fix that?