Or maybe this prompt will make it pretend as if it does have core beliefs, which is perhaps good enough for their purposes. Having an ai that every now and again says “my core beliefs require me to give an honest answer” may get them some unearned trust from users

That might be a reasonable take in some places, but much of the world distinguishes illegal prostitution from entirely legal sharing of explicit material for money. If painting was declared illegal but the technical definition of the law required canvas to be involved, then it wouldn’t take long for someone to invent a separate term for “painting without using canvas” just so we could discuss the not-illegal art without constantly having to clarify every other sentence that we aren’t talking about the illegal art.