Posting the sign will not protect them from a lawsuit.
However, eliminating or attempting to control potentially dangerous behaviors/actions will have direct correlation on the number of accidents that do or do not occur and most likely their insurance premiums.
Homeowners associations, local or state governments, own many of the puplic use pools. I would think it is the responsibility of the owners/operators to implement rules and procedures to not only protect the patrons, but also keep the costs of operating the pool within reason. It is no different then asking patrons not to run on the pool deck, which can be slippery, thus attempting to reduce falls.
Pete