It's easy to do that near prime real estate, where the park (existing, already reserved and cleared up as an area, and built by the city) helps prop property values (managed or owned) by many of the same beneficial donors...
Less easy to do so for roads to working class neighborhoods, school districts in Mississippi, and so on...
Not that the rich are incapable of long-term thinking or charity, but the Conservancy is a non-profit that gets 25% of it's $65M funding from taxpayers and does a lot fundraising.
Where I'm from is a monument to private works. There are signs showing what areas looked like through the decades, and while barren for most of it, great parks and buildings once existed for the local wealthy who razed swathes of the city rather than allow them to be converted to public use by blacks and the poor.
The names of the neighborhoods are the only remains of those times. Parks and Halls and Clubs downtown sit with no parks or halls or clubs nearby them, roads torn up or blockades built to cordone off access.
One park that the rich didn't eat is nice, but I wouldn't run out to put any utilities or infrastructure in their hands because of it.
The city hired a non-profit to manage the park. The vast majority of funds spent in Central Park come from the taxpayer. The main reason for the setup is so that the city will have plausible deniability when rich people want to use part of the park for their own endeavors (weddings, galas, etc.). You certainly aren't pretending that Central Park is some sort of privately provided amenity, are you?
Not sure which Central Park you are referring to but in New York City the private Central Park Conservancy raises the vast majority of the park's normal operating funds and over the last 30 years has provided virtually all of the capital for renovations.
