I would much rather have Central Park, an enormous and high-value piece of public land which is a crown jewel of the community and managed by the government as such, than a partial public-ish interest in "open space" or something on each privately owned lot, which is constantly being negotiated between landowners and a planning commission and ends up "meh," and where you aren't allowed to actually go, just look at.

I think this would be an important component of a YIMBY or Georgist future, to have public open space and park resources owned and managed explicitly rather than implied on each parcel.