I wonder if there is a language barrier or cultural difference here? In the UK parks are for fun and are not a means of getting from A to B. They exist to allow people to have fun and act in a carefree manner. They are not trainin facilities, thorofares or velodromes.
They're for fun over here as well, but they are not always "isolated" from the "public" sidewalk system. Some of them are what are known as a "liner park." Such as the rails-to-trial system of trails, and they are advertised as an alternative to getting from Point A to Point B.
And it is each person's responsibility to act in a safe, responsible, predictable manner. No one group of user has the freedom to behave in an unpredictable manner.
All my friends who have kids agree that when going to a park that the parents are responsible for the safety of their children, not some "stranger riding their bicycle" through the park.
Yes, I agree with everyone else in that cyclists, etc. have an obligation to minimize the risk that they present to other users, but that in no way removes the obligation of other park users to also behave in a safe, reasonable, and predictable manner.