This is what happened with dna testing at the beginning. Prosecutors claimed it was x percentage accurate when in fact it was hilariously inaccurate. People thought the data was valuable when it wasn’t.
I don't see that as particularly analogous. The average person will have had LLM technology in their own hands for years, whereas with DNA it was completely foreign to them and their only choice really was to trust the experts. And on top of that DNA testing matured and is very useful now.