I mean, to go from one to the other is fine imo. It's when you start stacking contradictory responsibilities that it becomes as conflict of interest. It'd be like making sr APD head of CC. You have to, ultimately, choose which side of the fence you're on. And if the responsibilities clash, then one side is getting neglected regardless. There's a reason we avoid these dramatic conflicts of interest.
Head of CC has to be able to debate and argue with staff without it potentially having an effect on his career in any way. Even if all those above him are responsible and mature enough to understand he's doing his job as head of CC, there's still the possibility that he would fear that it's possible to damage his staff career, and avoid disagreeing with staff anyways just by the nature of the dual position. Also, he could simply get folded into the staff community so deeply that he no longer actually represents civilians at all and starts parroting the Staff's consensus on every matter.
To be clear... This isn't about walt. I feel he was the best choice for head of CC, and I feel he has what it takes to be staff as well. This is about the nature of conflict of interest and why every well ran governing body of any sort does the best they can to avoid it, and when they don't, it always ends in institutional breakdowns and corrupts the system.