And that's what it comes down to I think. While London (I can't speak for Berlin and Tel-Aviv, I've never been) may be a big city, it's far from interesting at 3am. Hell, in most areas it stops being interesting around midnight or 1am, when most pubs close. You'll have a hard time finding anything that's more interesting than a seedy chicken shop at that point.
That the only public transport available 24/7 are buses, most of departs perhaps once an hour, probably doesn't help making a city active 24/7.
On the other hand, in London you'll see bankers having a large pint at 8am. So I guess there's that.
When I lived in NYC, it was the basically the same. Most subways switch to 1/hr after midnight, most parts of the city are sleeping. Union Square wasn't interesting at 3am, neither was Madison Square Park or anywhere around Central Park. There's stuff in SoHo/Tribeca, but not that much. At least that was my experience.
Obviously this can be affected by track maintenance, police activity, etc but that's not the norm.
Other rapid transit systems in the area are a bit worse, but still not 1/hr. PATH late-night headway is 35 minutes; Staten Island Railroad's is 30 minutes.
The commuter rail systems (LIRR, MetroNorth, NJ Transit) may indeed drop to 1/hr or worse per line, but that makes more sense for heavy rail.
[1] https://en.wikipedia.org/wiki/List_of_New_York_City_Subway_s...
https://tfl.gov.uk/campaign/tube-improvements/what-we-are-do...
They can't do it all week because of maintenance requirements - but London is pretty compact if you need to walk or take a taxi.
London can also claim a useful 24/7 service, with the night tube starting a couple months ago and the third and fourth lines (Jubilee and Northern) just opening up this week[1].
[1]: https://tfl.gov.uk/campaign/tube-improvements/what-we-are-do...
It helps that it's new and driverless.