Children start stuttering for neurophysiological reasons. However, as a child matures and ages with the experience of stuttering, psychological components definitely become layered on. These additional layers often in turn impact the manifestation of the physical speech. Most modern speech therapy approaches now attempt to address the psychology just as much as (if not more so) physical speech, for exactly the reasons and outcomes you described. Glad to hear you've had such a positive experience! Stuttering is as much a mental and emotional experience as a physical speech issue, and sorting it out is complicated. But very effective!