“The goal is to reprogram those subconscious beliefs” if only it were that easy. We can’t force ourselves to believe something we don’t in any sustainable way. While I believe stuttering can be rooted in trauma and hence be psychological in nature I don’t think cognitive restructuring goes deep enough. So while working on your beliefs that are often rooted in trauma can be useful, let’s not pretend it is as straightforward like you suggest. Our believes often change through experience. That is why a lot of stutterers when they get older naturally start to care less about their stutter due to different social dynamics and life pressures and hence stutter less