What proprotion of children live on inner city estates in huge cities? Most of them live on smaller estates in towns and cities other than London, Manchester and one or two others. My DGC's primary school in York draws it pupils almost equally from a seriously deprived city council estate and an area of privately owned interwar semis. I have walked through the council estate several times, you do see children playing out and doing all the things I listed above. The same applies to Reading and Oxford, 2 other towns I know.
Inner city estates have very specific problems. no-one would deny that, but they are only account for a proportion of children living in deprivation and many of those do, for example, have access to parks and playgrounds that they can safely access. They can run errands, buy ice creams, and, on occasion, see a bluebelle.