Hot springs are very dangerous as they can be scalding hot, and even if it's a cooler spring, there's risk of young visitors falling in and drowning. From a liability perspective, the risk isn't worth it. In addition to the safety of the guests at the park, you have to consider that the springs are part of a natural ecosystem, and should be protected from being destroyed.
As a huge fan of Yellowstone Park, I think they should provide reasonable markings/signings/blockings that prevent people from going too close to the hot springs. The last time I thought the markings were pretty clear, and I think they should be reviewed by the personnel on site to make sure they are maintained. Because the waters appear so placid, I don't think tourists, especially children, truly understand the consequences of having contact with the water pools etc. Some risky and stupid people are bound to go off the beaten path, but I think if I safe pathway is provided most people will stick with it, hence preventing dangerous mishaps.
I believe that the administration of the Yellowstone National Park should think carefully about how their visitors are able to view the hot springs. National parks are a precious resource, and the hot springs are one aspect of that. By forbidding people to go closer to the hot springs, Yellowstone will be able to preserve the landscape for generations to come.
I think a sign should be placed near the geyser, stating approach at your own risk. People are then allowed to get close to the geyser if they wish. If something happens to them, they had been warned and the park is no longer responsible for what happens to them.