Children's programming on OTA was dying well before KidsClick happened. As far back as 2002, Fox - having sold Fox Family and basically all of the Fox Kids program library to Disney - scrapped Fox Kids's weekday afternoon block and decided to lease out the Saturday morning block. 4Kids won that contract, of course. (I know 4Kids has never had a good reputation given their butchering, but the alternative was DIC! )
CBS and ABC's kids' blocks became rerun farms for corporate siblings around that time - I believe that CBS used the Viacom merger as an excuse to break off the deal it had with Nelvana for the CBS Kidshow and replace that with Nick Jr. reruns. But somehow, Kids' WB! managed to straggle into the year 2008...on The CW! There was hardly any cross-pollination with Cartoon Network either!
Local stations don't want children's programming other than what they're federally mandated to run anymore. They can only run twelve minutes of ads per hour, they can't run ads during the shows featuring characters from the shows (the cereal-hawking past of many cartoon stars wouldn't fly now!), and they probably wouldn't be able to get good-quality product anyway. As I've said before, 90% of the worthwhile content is owned by Disney, WarnerMedia, Viacom, and NBCUniversal. I can't imagine any of those companies are too eager to open up the vaults to over-the-air broadcasters they don't own - although the arrival of The Flintstones to MeTV indicates that attitudes might be changing. That show is a traditional all-ages bedrock, yes, but it's a highly valuable property owned by a company that long preferred to keep it "in the family," going back to when Turner controlled it. But as pay TV continues to erode, and even the future of the Boomerang streaming service seems cloudy, the childrens'/family entertainment behemoths may be looking into alternatives.
I can't imagine Sinclair gets along with other station owners very well anyway. They strike me as blustering, selfish, and not particularly amenable to collaboration.