Director Paul Greengrass helmed the next two films in the series, The Bourne Supremacy (2004) and The Bourne Ultimatum (2007), both starring Matt Damon.
With Matt Damon obviously not wanting to make that leap along with the universe, it makes sense to leave the actual Jason Bourne character behind and explore different aspects of the story.
Then again, Matt Damon did once say he had no problem with someone else eventually playing Jason Bourne.
Jason Bourne himself looks like he will remain on ice for the foreseeable future, but the larger Bourne universe remains ripe for further exploration.