As no two children are alike, there really is no one-size-fits-all answer to this. If a baby is smaller and less coordinated than might be typical for its age and fails to reach normal developmental milestones, there may well be underlying medical problems which require treatment. Not bringing in a child to see a health care provider in this case would almost be a form of child abuse. If the child is healthy, though, there is no reason not to let it develop at its own pace, although some forms of creative play may be beneficial to stimulate development.
In terms of meeting intellectual and social developmental goals, some people would argue that it is important for children to stay with their peer groups in school, rather than just developing at their own pace. However, there are problems with this approach for children who are significantly outside the normal developmental curve.
Child prodigies such as Mozart are quite rare. While it seems cruel for parents to push children into careers too early, in certain areas of music, sports, and dance, often talents do peak early; most aspiring ballerinas and gymnasts start taking class regularly by the age of 7 or 8 and are ready for intensive preprofessional training in their early teens. In such cases, it is important to have expert teachers work closely with the children to ensure that they are not being either pushed to fast or being stifled by inappropriate training.
Children who fall behind in intellectual development should not be "socially promoted" in schools where they will then constantly be frustrated by their inability to cope with schoolwork, but should be given extra resources such as tutoring and then placed appropriately for their skills and maturity level.