Is it nation(kingdom?)wide news? Our local sports coverage tend not to overlap, even when teams are geographically close or even when teams are in the same state yet geographically separated (such as Buffalo,NY and NYC teams). While the Yankees and the Red Sox have arguably the greatest US rivalry in sports, NY local sports coverage does not cover Red Sox games (unless it is late in the season and the teams are vying for a playoff spot), nor does the rivaly get much, if any, play on a national show. There’s little general interest and those who are interested can watch a channel devoted to sports, which cover everything. There will be some national coverage of exhibition games played in Europe (American football) and Japan (baseball), though. Perhaps it aslo has something to do with the sheer number of sports news outlets. Metropolitan areas, in addition to national sports channels, will also have a regional sports channel, plus every local news station (usually 4-5) will have a sports team. As I stated, living in NYC, I get 13 sports channels. Plus, nothing will cause even sports fans to dive for their remotes faster than a recap of a Kansas City Royals baseball game (especially if you are from Kansas City).
I’d like to also add that the audience of the shows listed in the OP, demographically, are poor targets for sports news. CNN Headline News does have a sports highlight segment; I can’t speak to FOX and MSNBC morning shows. CNN American Morning tends not to cover sports.