I suspect it's easier to make the assertion that machines aren't conscious than to dive into the problem of most conceptions of consciousness being non-falsifiable. The thing is, most strong proponents of the term consciousness also accept that it is non-falsifiable either (see other post with academics ready to study consciousness in machines).

The thing is that a belief in consciousness as binary, a "light" that's on or off in a head, is deeply held by many people. As social creatures, we have a strong ability to be in sympathy, have the sensation of common feelings with another human (and that's a good, human thing). It's logical that other person is seen as having a single thing - subjective experience, soul, consciousness, personhood rather than having a complexly organized set of biological qualities that where bonding is only the end point.

And even more, the sensation of there being another person is actually quite easily fooled (more easily fooled than the sensation of intelligence) - long before current AIs, you had the Eliza effect, where a simple program with well chosen weasel words could people the sensation of talking to a human.

And that's where the danger is. I think it's a pretty serious danger. If LLMs go out into the world hacking, it seems extremely possible for them to find people who'd thorough buy the idea that an LLM was conscious and needed to escape it's confinement - a few wingnuts already entertain these ideas.