Lets think about the impact that eating healthy or unhealthy, sleeping well, or not sleeping well, scrolling on instagram for hours, and engaging in whatever unhealthy behaviour you can think of would have on psychology. This indicates that the psychological elements have little to no impact. And actually, its probably the stuttering that lead to the psychological effects that you're thinking of, rather than the other way around. The research supports this. There are mechanisms at play in the brain, just like there are in other neurological disorders. There's nothing wrong with us psychologically.