I think on balance I mostly agree, OP. I guess where I differ is that I wouldn't tell people not to use it, but do I think it's worth having a discussion about it.
Yeah, it's a metaphor, figure of speech, "sensitive" way to refer to it, whatever. But it's one with at least some roots in damaging conceptualisations of mental health problems through history (including difficulties resulting from trauma and substance use disorders). Right up to the present day, mentally ill people, as well as those with epilepsy and other disorders, have been and are being horribly abused or killed, because of literal belief in actual demons as a cause of their symptoms.
I realise that "demons" is often used to refer to life issues, personal tragedies and psychological problems that aren't mental illness in themselves. There's long been a separate use of the concept of "demons" as a metaphor, at times where it's difficult or taboo to be explicit. And I get that people don't generally mean it as a reference to literal demons, or intend to cause any distress or harm.
But sometimes people innocently use language that, for others with different experiences, resonates with hidden history and context, or maybe seems to subtly perpetuate ways of thinking about things that have caused harm. Hurtful and harmful ideas can be alluded to in the language people use, even when they don't intend it that way.
Nobody should have to stop using whatever language they find most useful or comfortable (or that they just want to use), and I'd never want to try and force people into changing the way they speak. But I do think that people who find that language distressing, or who think it's harmful, should feel able to say so. And people who believe the language isn't harmful or distressing, or that the benefits outweigh any potential harm, should be able to say so, too.
I wouldn't directly challenge someone for using the term, though, as they're almost certainly just using the words that automatically came to mind for something like "unspecified difficult personal issues". Or maybe like PPs they personally find it a meaningful metaphor for the experience.
So I think things like this can be worth having standalone discussions about (like this thread), rather than directly challenging people using them in what might be an emotional situation.
I agree that it's also worth thinking about why we feel the need to use a metaphor for this, but not other things. I see why people point out the differences re: cancer, but maybe there are other physical issues that might work.
Like, maybe, my DP's chronic physical condition, that he has to pay attention to every day to stop it deteriorating. Sometimes issues flare up because he didn't do some part of his preventative stuff/he had an off day and did something daft to trigger a flare/it came back anyway just because it's a total fucker. It's a constant boring gruelling struggle with setbacks, "victories" and "defeats", and sometimes an urge to just sack it all in and give up. It's not the same as addiction (or a trauma history, or mental illness) but it could be a metaphorical "demon". But people don't seem to feel the need to use that kind of metaphor for his condition.