> GDP then it will grow if you strip out all public services, privatise those and make people pay for it
No it won't, because people won't pay for it. They can't, so to get ahead of your next argument: it doesn't matter how necessary those services are, they can't pay. If doing without means a city dies economically or even if it means people start actually dying then that's what it will mean, not more GDP.
Read about the century before and after Irish potato famine to see an example of just how bad it can get, while still not resulting in GDP growth.
> What even means to improve economically?
Having the ability to do more, on a bigger scale. Think of it this way: there isn't a city on the planet that wouldn't benefit from rebuilding itself (in practice increasing the rate at which it rebuilds itself). Lots of houses, businesses, ... are old and have huge problems that need fixing. Most places could use a lot more houses. And then, there's no shortage of ideas for improvements. Wouldn't you agree it would be great if the London metro had the same density all the way to Birmingham as it has in the center of London? If the New York metro extended into the state? If medical care really was universal, cheap, fast and thorough? If there was a vaguely usable train network in Europe (by which I mean that it would be realistic, and cheap, to use European trains to go from, say, London to Rome)? To say nothing of the fact that in 90% of the world, if you brought people's living standards to Eastern European levels, that would be increasing them. That certainly seems worth doing and requires more economy.
These are extreme and perhaps unrealistic examples, but, yes, that would be economic improvement. And yes, these things would improve nearly everyone's lives.