Yes Tom, that's a very good question, but the tot lots at parks AND schools ARE public property. In Oregon, the fresh and salt beaches ARE public property, but I do not hunt there without a written paper from the State Parks Department, and it's relatively easy to get one too. In fact if there are no statutes or laws against doing so, then it is perfectly legal and prudent to hunt anywhere in the USA. I have contacted not only the public parks departments in several states, the local magistrates, city and county ordinances, and the school districts, I have also contacted legal counsel, meaning an attorney - regarding the subject. It is not illegal to hunt on public property anywhere in the USA unless there is a legal restraint disallowing us to, to include Federal property. If there are no restrictions then there is automatically written permission to hunt there, and it is "pro bono" too. I (we) do not need a special writ to do so. It is pervasive and all-inclusive in these cases. All we need is a copy of the law, and we need to take it with us too, because some cops don't even know this.
The fact remains though, that if it's not yours and you take it knowing that it has not been abandoned, and have a normal healthy conscience that tells you that you can also with reasonable prudence find the owner, you are stealing, and certainly not borrowing. I have found the owners of some things I've found, but that is seldom a viable option, and therefore it is lost, and no longer owned. This too is a law. In Oregon, there is also a very unique law; if you neglect to care for your (real) property or never improve it past it's pristine or natural state, someone else has the right to take it over via homesteader's rights. This does not include property other than real property though.
Additionally, the "State" is not the "State of "democracy" in America, or the "State of Communism or Marxism" in America, it is the "State of the Republic" in America. In a Republic we are bound to our laws and agreements oftentimes by vote of electorals, not by direct representation, and this is because America is TOOO big to be operating as a true "democracy" to start with, however Russia is, and it is in fact a true "Democracy". If we did operate as a true democracy, we would be voting and deciding on each and every issue and therefore we would never have time to go to work, which is what is happening in Russia quite often now.. The whole country would go to Hell in a handbag in very short order if we tried that. True democracy is called "government by mob rule" because of this fact, and it and Socialism are impractical and unreasonable and self-defeating because of this fact. Government 101. This is why we need a Republic. It's also why we have one.
Again, taking or claiming something without written permission by virtue of being written in the law or by pre-agreement, or by special required written permission, or by virtue of abandonment of previous owner, or by our own current possession, is a crime and a sin, and in fact, both.