Thing is they did change her story. Redo of Mad Monk and Monster Men had her as law Student that Bruce knew and in the end she left to the peace corps pre new 52. When she was brought back for Snyder she retained some of the stuff established in the updated Mad Monk and they added their connection to being her knowing he's Batman and that she knew him now when they were teens and so forth, so her connection to Bruce is a lot deeper thanks to her story with him and his memories being gone.
Also Andrea basically is Julie, she has her background to a T. Dead mother, dad working with the mob, father killed by said mob. The only difference is she goes on a revenge spree.
Both Selina and Talia are not stable. And if we get into it having a stable relationship with Bruce could be something intresting over all because it would lead to some important drama.
I don't think the attempt at a stable relationship with a normal woman is going to offer much for the woman in question. Beyond the obvious (he's rich and hot, and the mystery man crime fighter thing is sexy), what does a normal woman gain out of a relationship with Bruce long term? Even the versions of Bruce that are more emotionally stable than others? His life is dangerous and he's never going to change or stop, not completely, it's not in his character to ever do so. The novelty is gonna wear off, he will either get bored with her or she will understandably get frustrated with him and the stress would be too much. It also applies to the fandom that ships Batman and Wonder Woman. What does he offer Diana? She is often set up to "fix" him, but what does she get in return?
Selina is no more unstable than Bruce. Probably much more stable than some versions of him, and she's already on his weird wavelength. Despite King's weird ass execution of things, she clicks with him better than other options and offers something unique compared to other mainstream DC heroes and their primary love interests. A match with a normal woman might have Clark/Lois or Barry/Iris redux going on.
The femme fatales would just enable Bruce's bad behaviour. What he needs is to find his own self-worth and make a life for himself as a fully rounded individual. But comic book fans want him to be dysfunctional.
I can't see how women would be attracted to Batman--other than as an abstract concept. In my mind, Batman would not be seen except in shadows or from a very far distance. Any photos of him would be grainy or blurry. He would never talk to people close up and he would speak in as few words as possible, if at all. He would do all the close contact work as Bruce Wayne or in one of his many aliases.
It's hard to disentangle, guy who dresses up as Bat from dysfunctional, yes, even in his lightest incarnations.
But the biggest problem with an ordinary spouse is that in order for a love interest to stick they usually have to be both useful to the narrative and the hero's equal in some way. Lois isn't Clark's physical equal, but she's as good a reporter as he is. Barbara and Starfire both match Nightwing in significant ways. A civilian wife at home for Bruce serves no function in a story that Alfred does not already provide more effectively. Without another function she rapidly becomes just the thing that impedes the audience from getting to the part they want to see.
And of course there’s always someone like Vicki Vale for Bruce to talk to. Nothing romantic needed, but that said, I suppose Bruce could be considered someone who... longs for female companionship, regardless of how much he tries to hide his feelings.
Vesper Fairchild.
Wait. Which one was the psychologist?
Vesper is a talk show host.
Chase Meridan is a psychiatrist. https://dc.fandom.com/wiki/Chase_Meridian_(Burtonverse)