We now face a very sad situation with our DD as all her friends will be going to the local school.
Loss of community is one of the fatalities of the current system. It's not just a nursery child losing her friends. It's a whole family losing the neighbourliness of shared experience with other families on your street. For parents, it also portends years of struggling without local support, without being able to exchange favours, pick up each other's kids, when family or work emergencies strike.
Schools are traditionally the glue holding a community together. Long ago, churches helped, but they're discriminatory and don't really help foster community in a diverse areas like London.
Op initially listed her six closest schools. In London, the council's two-mile radius is 3 or 4 communities away! No local childminder will drop off or pick up there.
My DGD scraped into her nearest school off the waiting list a few years ago. Now, most families on their street haven't a chance of getting in. Nor, of course, will they get the 'next-closest' or 'next-next closest'. They'll get a dump school miles away (schools where teachers 'yell at' the nursery and reception children 'a lot'. Those are the only schools with any vacancies.)
I already see some of these parents losing interest in local community efforts, even fetes, parties, plantings... as they bitterly start to research other options. It's sad.
As others have pointed out, most people want a decent local community school, only a minority are jockeying for top-rated cream of the crop.
I liked nlondad's story of Islington opening bulge classes in the south of the borough whilst vacancies remained in the north. That represents a true respect for community that, sadly, we're unlikely to see in Haringey.