This is my opinion in response to the question you asked:
Determining whether ownership registration should be applied to urban green infrastructure depends on the unique circumstances, values, and objectives of the community. It's crucial to find a balance between the interests of private entities and the overall public welfare to ensure the sustainable development and effective management of urban green spaces. The decision-making process must consider various factors such as environmental preservation, community accessibility, and the potential socio-economic impacts of ownership structures. By carefully weighing these factors, communities can establish policies that promote responsible management of green infrastructure while addressing the diverse needs of residents and promoting the long-term well-being of the environment.