They do, at least in the US, as viewership has dropped and leagues have struggled to attract younger viewers.

- The NFL provided a SpongeBob-themed alt-cast for a game last weekend -- https://www.youtube.com/watch?v=TcHIfPERX0s

- F1 has a similar graphics package+commentary for kids -- https://www.youtube.com/watch?v=-xUBfP2-BEA

- The NHL used their new-ish player position tracking tech to produce a real-time (or at least near-real-time) game themed to Big City Greens last year, and is set to do another in a few weeks -- https://www.youtube.com/watch?v=cCupuTnNmQ0

- The NBA has similar position-tracking tech, and used to animate a game on Christmas, with Mickey Mouse watching -- https://www.youtube.com/watch?v=wE68Q4oPcPs