A golf course, private or public, should not be used as a substitute for child care. If the parents can't arrange adult supervision or otherwise ensure proper behavior, their kids have no business on the course. Staff, members, and customers should not be required to assume the responsibility of the family. Not only are most inadequately qualified to act appropriately, the legal environment is mostly hostile and often punitive when they intervene (reference the public school system).
If clubs wish to provide some of these services, all the more power to them. No doubt that some members or customers will be drawn to these kid-friendly facilities, while others will vote with their feet and gravitate toward those which provide the golfing envrironment they seek. I do think that the First Tee and other similar organizations are doing God's work.
As to junior golf being the future of the game, I am not aware that it was responsible for the rapid growth years. Most golfers I know picked up the game later in life, after playing team sports. Personally, I think the future of golf lies in a sound economy, a growing population in the demographics which support the game (primarily adults with disposable income), and accessible, affordable facilities.