I got this question after watching some cutscenes from Lego Star Wars: The Skywalkers Saga
Anakin just killed Dooku, and Grievous walked in, (unlike the movie) and the duo of Kenobi & Skywalker assume a fighting pose, with Anakin holding Dooku's saber.
Why didn't this happen in the original movie? Not the Grievous part but Anakin keeping the lightsaber to fight Grievous later, I mean.