Some of these properties are literally little more than empty lots. I’d think those could be turned over to neighborhood associations to maintain if the neighborhood considers it a priority. Other than mowing and trimming or the occasional coat of paint on playground equipment, there’s really not much to maintain on many of these parks.
We have Helms park in our neighborhood (more accurately, the neighborhood we border with). It's a city funded park, but beyond the playground equipment an a load of mulch they dump every couple of years, we've never seen the city doing anything to maintain it. The neighbors take care of mowing, trimming the trees, and repair the equipment. We plant flowers, paint the grills, rebuild the signs, and even mend the walkways. Our kids like to play there, so we feel compelled to contribute.
In the back of the park, the neighbors have built a small fenced in community vegetable garden, that unlike what Henderson fears in his district, no one grows pot in.
Community parks must be supported by the communities that value them, public or private.