It's a tool, not a source of empirically valid data. No one's going to 'get used' to LLMs being cited as sources of factual information any more than they'd complacently accept someone's Monte Carlo simulation or a hypothetical thought experiment being cited for the same purpose.
If you claimed that your source was The Onion, you’d get similar responses. You can make a claim, with no source, and expect the traditional answers. When your source is a “known to produce crap” source, what would you expect to hear?