People in manhattan can go west, south, east, north anytime anyhow with few or no connections. People in the outer boroughs have to many times go via Manhattan to get where they are going.
The Paris example is somewhat skewed, though, because Paris proper is comparatively tiny – just 105 km² and 2.1 million inhabitants. Compared to London it's basically just Zone 1 and a few bits (definitively less than half) of Zone 2.
Having said that, yes, it could still well be (too lazy to figure it out properly) that inside this city core the Paris Metro is still more dense than the Underground in London – but on the other hand beyond that, where the vast majority of inhabitants of the whole urban agglomeration of Paris live, you have similar problems regarding radial travel as elsewhere:
Yes, it requires everyone to live in small houses or apartments adjacent to each other without large backyards and garages for cars. Hence it working well in Tokyo.
Tokyo can exist in Japan because of some properties intrinsic to Japan which I'll get flagged for pointing out. The reason I tried to emphasize "expensive" is because those cross links are probably where a lot of the crazy property tax in NYC is going.
