In the Daemon Lover ballad itself, the Devil doesn't corrupt the woman so much as he reveals her.
We learn first that she previously made a promise to another man, and then broke it. Which in itself is pretty reasonable - he was away seven years, he might have abandoned her or died, she can't waste her life waiting, women often had to marry to survive. But she also takes almost no persuasion to leave her current husband and abandon her children. She is quite willing to do it! And the only question she asks of "James Harris" beforehand is how much wealth he has to take her to if she goes with him.
He deceives her, and she lets him deceive her because she wants to believe him. But the deception and her response to it reveals her true character.
I think the same is true for Shirley Jackson's James Harris. On one hand, when his name comes up in the stories it's associated with deception, self-delusion, previously certain things becoming unstable, loss of identity... But on the other hand, he's a disturbing figure in part because he serves to reveal the truth.
In "The Daemon Lover," the woman's search for James Harris shows us how lonely and unwanted she is, and how obsessed with social approval and validation; and it shows us the unkindness of the society around her, and lays bare female husband-hunting as a frantic race to avoid being relegated to the status of a scorned and irrelevant old maid.
In "Like Mother Used to Make," it takes only the brief nudge of James Harris making an incorrect assumption to drive David and Marcia's behaviour. David could so easily correct the assumption and stop her. But he doesn't. He watches his apartment and identity and life be taken over and makes no move to stop it, for fear of being impolite or having to assert himself. And we also see how Marcia doesn't want to be herself and doesn't like her own disorganised, dysfunctional life, but doesn't see herself as capable of organic change - so she has to appropriate someone else's life instead. (I wonder if David ever sensed her jealousy/covetousness before the beginning of the story. I wonder if he refused to recognise it on a conscious level and kept inviting her to dinner anyway, because it would have been rude not to.) James Harris's appearance just reveals certain tendencies that the characters have, and sets them into motion.
We see it in the other stories too. In "Elizabeth," obviously, he's used to show the extent of Elizabeth's unhappiness and the way she externalises it or turns it into self-delusion instead of recognising it. In "Seven Types of Ambiguity" his presence allows the man to buy the book and therefore reveals the man's insecurity and pettiness, the way he uses his newfound wealth to engage in a power-play against someone who helped him and treated him well. Even in "The Tooth," Clara's growing disorientation and eventual loss of self feels like something that already existed is being brought to light.
(It's kind of interesting with the context of James Harris being the Devil, and the Devil being referred to as a deceiver and the Father of Lies.)
And so many of the stories also revolve around seemingly stable situations being disrupted, or people's idealised images of things being shattered. Some of them don't feature James Harris directly - but he's there in that disturbance, in the sense of things not being as settled as they seem.
Also, this all means that James Harris is Shirley Jackson's representative within the stories. Someone who disturbs and unsettles the world of each work by revealing various truths about the characters and the society they inhabit.
