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.
This is the DC map:
https://www.wmata.com/schedules/maps/upload/2019-System-Map....
If two friends move to the outer edges of different legs of the system, then your travel time and inconvenience multiplies a lot.
It is the same reason Manhattan is so popular compared to the outer boroughs:
https://new.mta.info/map/5256
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.
Now take a look at a map of a good subway system:
https://www.tokyometro.jp/en/subwaymap/
Paris is another good one:
https://www.ratp.fr/en/plan-metro
You can get from anywhere to almost anywhere without having to go to the middle of Tokyo.
The Tube is okay, but still has the problem of the lines not connecting once you get out of a certain radius:
https://content.tfl.gov.uk/standard-tube-map.pdf