Rebirth Deathstroke's obsession with Damian had nothing to do with him being a TT's villain.
Slade simply loves Damian because he can access the love he craves and feels [yet doesn't know how to express with his kids] with Damian because he is like Slade. Which I sort of can see.
Priest states that he hints at Damian's parentage all through his run! I didn't get that and I'm glad I didn't. That seems OTT
https://www.cbr.com/damian-wayne-deathstrokes-son/
In an interview with Newsarama, Priest revealed that he hinted at Damian's parentage throughout his run. "'The World's Worst Dad' is about a man who loves and desperately wants to be loved but is capable of neither. So, he does skanky stuff like put a hit out on his daughter so he can spend time with her. And, in the latter part of the series, Deathstroke clearly falls in love with Damian Wayne. I hope fans can understand that, I hope they got that. Deathstroke loves that kid and can access that love in ways he cannot with his own children because Damian is so very much like him."
DC however wasn't thrilled with Damian being a Wilson so Priest did the next best thing. 'Altstroke' The perfect Slade Wilson
http://www.multiversitycomics.com/in...est-interview/
DC feels more like Gene Roddenberry’s utopian view of the future, where kindness, forethought, and patience are the rules of the day. How does Deathstroke function in that kind of environment? I mean, I had Slade kill Power Girl’s dog in issue #17, and that was a major push. So far as I am concerned Slade, not Bruce, is Damian Wayne’s father. I mean, I get why DC made the call they did, and Damian is not *my* multi-million-dollar I.P. to gamble with, but I lobbied hard for another, in my opinion, more daring choice that would have shaken things up, enraged fans, and launched dozens of exciting stories.
Maybe if “Deathstroke” was published under their Black Label [imprint] there’d be more flex in terms of what the character could be.
This was my real motive for AltStroke. Since we were about to take our bow, I thought I’d like to write the character the way he should, in my view, actually be portrayed: as a totally ruthless, unlikeable bitch. And Damian IS his son (Laughs). Now, could AltStroke sustain his own monthly title? I actually think yes in the short term, not in the longer term because eventually he’d either kill everybody or kill himself or we’d fall into the cliché of constantly contriving reasons he wouldn’t.
But at least Deathstroke, as I’d have actually liked to have written him, made a brief cameo before we turned out the lights.
https://www.cbr.com/dcs-dark-multive...t-deathstroke/
Instead of being a clone or a copycat of the main Deathstroke, the elder Wilson has been marooned on Earth from the Dark Multiverse. But before he arrived here, he was truly the most ideal killer. After the Dark Slade kills his world's Batman, Damian Wayne and Wonder Woman show up alongside him, basking in the bloody glory. With Damian sipping on a juice box, the issue pays homage to a story that teased the idea that Slade could really have been this Robin's dad.
In this reality, Slade he is Damian's father, and Wonder Woman is his mother. Together, they make up Slade's perfect, deadly family. After Batman's death, the Teen Titans, his traditional rivals, show up, and Slade and his family prove just how deadly they really can be.
this Slade Wilson accomplished more in a few pages than his counterpart has in his entire career. Even though the main Slade had elaborate plans to take down the Titans like the one he used in "The Judas Contract" storyline, he and his family take out the Titans and Batman with a straightforward and practical approach and effective allies a family who get the job done.
The deadly Dark Multiverse trinity of Slade, Diana and Damian accomplish far more than the real Slade ever did with his children Jericho and Ravager. With a demigoddess for a wife and an elite assassin for a son, the Dark Multiverse Deathstroke is living his best life.