Oh yeah, Canary's history is weird as f**k. She started out as a member of the JSA on earth-2 (well, she was introduced before separate earths became a thing) and had a daughter who was put in a coma for.....reasons. I think the powers she got (from that magic spell mentioned already or whatever it was) were too dangerous or something. And Canary starts dating the Green Arrow of earth-1, who was much younger than her, and she moved from earth-2 to earth-1. Eventually she has her mind put into her daughter's body while she and Ollie just keep on like nothing happened and......it's just weird as hell.
You've got great points, (I usually dont like crossover pairings either) but I don't think history is going to be enough for Dick's former relationships to carry any serious weight again. We're not talking Lois Lane here.
We'll get teases, but I don't think the trigger will actually be pulled on either again.
As long as Babs is starring or co-starring in her own book she's going to have writers who want to do their own things with her. Which means the relationship between Dick and Babs is always going to be going off course because their respective writers have their own stories and ideas to tell. We've had teases about them getting back together but it hasn't actually happened (for more than two minutes anyway) and won't ever get beyond that point, for logistics reasons if nothing else. We saw the kind of problems this can cause in the Superman-Wonder Woman relationship; they were part of the same editorial office, but their writers couldn't play with the dynamic for fear of stepping on the toes of the other book's plans. And we all know how bad DC is at communication.
And as long as Dick is a part of the Bat office and that office is determined to downplay everything about Dick that didn't come from Gotham, a relationship with Kori isn't happening either. DC likes to pretend that Dick's time under the Titans office didn't happen, or at best that his involvement with the team went no deeper than Bruce's involvement with the League (a job, not a home). So Kori is out as a potential love interest too, simply because DC doesn't seem to want the reminder and dont want fans to remember how vital the NTT era was for Dick's character and development.
Now, that's a problem with Karen too, and obviously this pairing I'm suggesting isnt going to happen under current management and is just for lol's. But Karen-Dick offers a few benefits Kori and Babs don't. For one, DC is strengthening the ties between the Bat and Super families. We see Bruce and Clark cameo in each other's books often, and among their "kids" we have a lot of connections too: Babs-Kara, Damian-Jon, Tim-Conner. Putting Dick and Karen together pairs each of the prime Bat kids (aside from Jason) to a Super. It's the World's Finest and DC seems perfectly happy to push that dynamic right now.
Karen doesn't have a book these days and is unlikely to get one (unfortunately). The best she's likely to get is a spot in the JSA when they eventually return. And there's little room for character development in a team book, especially one with a roster as big as the JSA usually boasts. So pairing Karen with Dick, putting her in the Bat office as a part of Dick's supporting cast while loaning her out to the JSA, actually gives her a place where she can get some character development as well as extra panel time. And just because she's dating Dick doesn't mean her subplots have to revolve around their relationship. Additionally, Karen's (presumed) role with the JSA offers an easy explanation for why she doesn't just swoop in and do all the work for Dick. While he's fighting his villains, Karen's with her team fighting their's. Or on her own, or with Harley, or whatever. Point is, Karen's a busy woman and she doesn't have time to fix Dick's problems for him (as she shouldn't).
Also, one of the biggest problems with Babs and Kori are the fans of the other woman. Each pairing has a pretty substantial fanbase and neither will really be thrilled to see the other side "win." By using Karen, no one gets what they think they want but everyone might be able to agree on the new pairing. And Karen and Dick bring new narrative options to each other. Through Dick you can involve Karen in mystery and spy stories and other street level narratives where the problem can't simply be solved with super strength. Through Karen, Dick gains easy access to sci-fi and science fantasy narratives. DC seems perfectly willing to let Bats do high concept adventures, as long as they're with a Super.
And Karen would benefit from the higher profile. She's not nearly as big an IP as Nightwing is, so the tie to him will only help increase her visibility (granted she should be getting more time with Clark too). And as long as she's written properly and not as a 1950's damsel in distress, being a supporting cast member and love interest isn't going to "reduce" her as a character. Plus we'll likely have her punching things in JSA, so between the two titles we could have a fairly well rounded and developed Power Girl; possibly more than we would if she were only in one title.
Plus I just think they'd have a great dynamic. And really, who else is a viable love interest for Karen friggin Star? That woman is a force of nature and would just decimate most men.