There is certainly variability within the stuttering community in what stuttering sounds and feels like as well as its trajectory across the lifespan - so I'm not at all criticizing you for sharing your own experience. However, the advice that you give in your first two paragraphs is not supported by the majority of our current research and anecdotal evidence. Awareness of stuttering does not create issues for a child, but as long as that awareness is raised in a neutral way, it can empower them to understand what's happening when they talk. If parents/others who care about them don't do this, others will bring awareness to it but likely in negative and shaming ways. Much better to educate kids in safe spaces so that when others stigmatize them (inadvertently or deliberately), kids will be able to recognize that the problem is not with them but rather with society. Stuttering is not curable for the vast majority of the population, so it's misleading to represent it as being that way.