I was listening to the excellent if sporadic Transporter Room 3 podcast, and the hosts suggested that the reason for Fuller's departure is because CBS is still "your grandfather's network," meaning it could be they didn't agree with Fuller on elements they may have considered "edgy" or "out there," like the gay character and, if I'm not mistaken, a rumored Muslim character.
I tend to think this is the reason Fuller left and/or was booted. Supergirl has become a show that doesn't hesitate to feature a recurring storyline about the coming out of a main character and a very preachy episode about climate change. CBS owns The CW, but they care far less about the content on the latter than the former. They likely felt Fuller was going "too far" with certain elements and they didn't want to risk anything with their streaming platform's flagship show.
The problem is, they may have very well doomed Discovery to failure by trying to be too careful. Time will tell, but the hope that was restored when we learned this was in the Prime Universe was all but completely eroded when the show got pushed back and when Fuller's departure was announced. I didn't think Fuller was the best guy for the gig or the only guy who could do it (would've preferred Manny Coto or, best of all, Ron Moore) but the creators of Pepper Dennis helming a Star Trek show doesn't give me much hope.