Because that's where the money is, and the days of establishing supporting characters/love interests that will be cemented and developed are long over because new characters don't gain any traction anymore.
Diehard shippers tend to be a loud minority online for any franchise (and are often the worst element of any franchise), but at the same time so are the people who voice dislike for certain pairings and relationship drama. The wider audience loves romance mixed in with their fiction. As many people on here say they are sick of Bat/Cat because of Tom King, it's still showing up in a new film trilogy because it's very popular among the audience that matters. It'd be the same with Dick and Babs and Kory should he show up more in other media installments for either franchise. The creators involved would likely use Babs or Kory because those are the popular ones they'd be eager to use and not many people among fans or casuals would be likely to care about a new love interest.
DCAU was definitely an early case of "subverting expectations for the sake of it" and it not resulting in anything good. Like we had the shocking reveal that Bruce and Babs hooked up...ok, and? It avoided the popular pairings for either of them that people actually liked and grossed out everyone. Which was the intended goal, but it accomplished nothing else. Bruce and Barbara's interactions in Beyond would barely change if that never happened.
It also may spring from Timm not liking Dick very much, he didn't give many vibes that he cared for Dick in the "House and Garden" commentary on the DVD release ("This Little Piggy" is also very illuminating for his feelings on Wonder Woman). It may be for the best that Dick and Barbara don't appear to be in The Caped Crusader as of yet. It's definitely going to be Bruce Timm unleashed with nobody to tell him no, so odds of it being bad have increased.