After Time Warner bought Turner Enterprises(the owners of TBS, TNT, and Cartoon Network/later Boomerang) they struck a deal to make the Looney Tunes exclusives of the Turner channels. Which meant long running airings of the Looney Tunes on Nickelodeon and ABC, among others, ceased in 1999. The Turner channels ran the Looney Tunes with much fanfare until about 2004, when after the disastrous failure of the film Looney Tunes Back in Action WB decided to "retire"(so to speak) the franchise, with the exception of DVD releases very little was seen and heard from the property for several years. Since then they have had new shows and the original cartoons have come back to Cartoon Network and Boomerang, but they are a bit more sporadic than they used to be. There are several reasons they aren't really relevant to todays kids, but I feel the big reason is the WB-Turner agreement. WB could've easily continued to license the cartoons out to different networks and platforms that would've kept the characters in the public eye, but I think forcing them to only be available on a few select platforms really hurt the brand.
Though to be fair the original Disney cartoons, the Mickey series, the Donald Duck series, Silly Symphonies etc, were all run on television until some point in the late 90s-early 2000s until they too disappeared. Unlike the Looney Tunes who have had hundreds of their cartoons released on easy to come by DVD sets, the Disney content was only available very briefly on limited sets that quickly became very expensive. And there's no corporate fuckery going on either like there was with the Looney Tunes/WB, it's just Disney is weird for some reason. I'm holding out hope all the old cartoons and the early television productions will be made available on the new Disney streaming service, but who knows.