I think, this question is strongly culture oriented.
In France, transport and land use planning were very stringent. Nowadays the planning is not very compelling. With a broad definition of public space, I would say that a powerfull planning agency is needed in the French context. Mainly to create "green amenities" in the deprived areas (in Paris and Lyon, the Eastern suburbs).
The COVID-19 has tested the reality of our cities. Although it is now necessary to maintain distance, many districts and cities hardly allow this, even in generally well equipped European cities. Car-friendly cities have long been the focus of urban planning, leaving little space for pedestrians who could barely keep a distance of two meters. High-quality open spaces are rare in many parts of the city or have been privatized. As a result, it is difficult for many city dwellers to spend time outside their home and a particular challenge for those who live in small apartments with no outside space. This situation will worsen dramatically in the summer when people just want to leave their hot apartments to find crowded parks.
I think also that the concept of "Place Attachment" could be of a great added value to the evolving aspect of public open spaces and their major role in society.
Article Understanding the process of parks’ attachment: Interrelatio...
Public space takes its importance from activities that take place .. so, in order to evolve a public space we need to:
First, making a public space that suits the citizen' desires .
Make it an open access space by placing it in secure and open area ( hear we are talking about physical, visual and psychological accessibility to that space)..
Involving citizens in building that space and getting care of it and with time it will takes sens and signification by creating what is called a "place attachement" as mr amine Moulay said ..