Actually, Justice himself tells us that most Spirits don't care about mortals or the mortal world. Even Justice spirits don't seek people out. They are abstracts within the Fade, and content with that. It isn't until you engage a spirit, somehow, like the one in the Mage Origin, that it takes notice of you and has to be dealt with. Like a cow. You have to do something to make the cow decide you need to be dealt with before it is an active threat. As the Baroness did with Justice. And had Justice been able to deal with the Baroness in the Fade, that would have been the end of it. Justice would never have sought to enter the mortal realm on his own. It held no appeal. A demon, however, is an active hunter. Like a wolf. All you need to do to be in danger from either is to be in their hunting range.
So, yeah, the Cow vs Wolf analogy is spot on.
I've never been convinced that the demons have been uniformly active hunters. I'm not talking about 'oh, sloth demon there doesn't care' as the exception that disproves the rule: I've never been convinced the rule actually exists, as opposed to being a tautological classification. All bad spirits that act are demons: we know they are demons because they are bad spirits that act. Rinse, lather, and repeat.
Without some way to figure out just how active spirits and demons actually are, the claims seem unsupportable. It also blurs capability with willingness or desire to act. The Forbidden Ones, for example, don't seem to have actually instigated contact with Tevinter or the Mortal realm: they have been reactive forces to someone else's initiative. Why are they considered demons, rather than aggrevated spirits? Or let's take demonic politics of those implied but never seen fade heirarchies: if a demon of desire doesn't attempt to cross over/posses/interact with the material world because of fade politics, is it not a demon anymore? When a spirit takes an active hand in the world, is it now a demon?
And this is without the greatest issue of the Fade: that no one, not even the spirits, seems to be an actual authority figure on its history and nature. Spirits don't know the truth. Demons will claim whatever. No one has ever claimed to know the origin of the distinction between spirits and demons: is it one the fade beings presented, or the humans(elves?) created? I consider it very possible that the fade beings picked up the spirit/demon distinction from humans, rather than the other way around: spirits like Justice might identify demons as demons because Humans introduced the distinction, rather than humans learning the distinction from the spirits and demons themselves.
I think the demon-spirit classification is flawed because it confuses two different distinctions. The first is the distinction of nature: spirits are this type of benevolent emotion, demons are this sort of bad emotion. I suspect this is ideological, not structural, distinction. The second distinction, though, is the distinction of effect: demon seems to be the shorthand for 'bad aspect that does bad things in Thedas.' But what about bad aspects not trying to enter into Thedas? Or a bad aspect that has a good result?
A retroactive classification is unhelpful. An ideological classification is misleading.