Arguably the biggest social problem to effect public space is massive amounts of car traffic. That causes orders of magnitude more problems than any of the things you mentioned. Our most important public spaces are overrun by cars that mix well with nothing.
I've lived in various areas, currently a bit further out in Zone 3, which means I should add rampant fly tipping and unlicensed/uninsured/abandoned cars to the list.
Eliminating these nuisances from an area is a costly business. It requires round the clock security, extensive CCTV monitoring, constant maintenance and adherence to the "broken windows" philosophy.
It is essentially a luxury, which private property owners bestow upon their 'pseudo-public' spaces. The public would be outraged if councils sought the funding, through taxes, to apply the same to truly public spaces.