A city the size of London would have circa 2,600 babies born every year that would qualify as gifted (top 2 percent /130+ IQ). You could have several schools all over the city for gifted pupils without the need for boarding.
I know that some definitions of giftedness talk about the top 2%, but that's actually a very low threshold - you'd be talking about 3-4 kids per year group in an average secondary school. While those kids are obviously very bright, I really don't see why they would need specialist provision. In any case, special schools for the top 2% just sound like another version of grammar schools, and I think there is substantial evidence that they don't really work as they end up full of heavily tutored middle-class kids rather than the brightest.
I had assumed that those arguing for special provision were thinking more about profoundly gifted children, not just the top 2%, most of whom will be well within the range of normal. There would only ever be a few of those kids at any one time, so I really can't see how you could avoid boarding.
I have been thinking about this thread and while I am very firmly of the view that NT children who also happen to be gifted are best catered for in mainstream schools, I suppose that there might be a need for some sort of special provision for those who are twice exceptional. I'm thinking particularly of those gifted children who really struggle to relate to their peers, as I suspect that many of them are on the autistic spectrum, whether or not they have been diagnosed as such. As far as I'm aware, most of the existing special school provision doesn't cater well for kids who are high academic achievers, so perhaps that needs some thought.