There are definitely fancier HOAs with bigger and nicer parks and common spaces than the others, and I don't think it's because they have different city rules.

HOA style commons solutions means a city becomes thousands of micro, private, exclusive spaces.

Perhaps better than everyone sitting in their homes getting amazon deliveries every few hours.

but this isn't what people mean when they say public community spaces. We need interconnectedness across income, ideology, generation, education, etc, for stable democracy.