I feel compelled to defend the New York map. Not as perfect — far from it — but as better in many ways than the abstract maps more commonly seen, and in particular, better suited to the geography of the city than it would be if produced by following these rules or mimicking the London masterpiece. I suppose it comes down to the New York map being the result of different cartographic philosophy.
What the New York map does that many others don't is integrate the subway diagram with the aboveground geography and roadways. New York, the city, is uniquely suited to this approach. Its "core", rather than located at the center, is shifted all the way west/leftward, and unusually, it's not a roughly symmetrical square or circle, but a thin, vertically oriented rectangle. Moreover, unlike many of the world's cities, Manhattan's streets are largely laid out on a grid, which the subway lines follow. As a result, the map is able to exaggerate Manhattan's size — and thus enlarge its portion of the subway map for clarity — while also providing a reasonably accurate and proportional integration of the subway lines with the main north-south and east-west streets. In short, when you emerge from underground here, you not only know where you are in relation to the subway system, you also know where you stand in relation to the city. That's not something the Underground map and its imitators do well.
Or at least you can know this latter relationship. The New York map does not do the best possible job of making the street-grid clear (the roadways are delineated in a faint grey, for example, and are easy to miss). And you do need to have a rudimentary grasp of the grid to know what, say, the corner of 42nd and 6th means if your destination is, say, 40th and 7th. In this regard, the map is friendlier to locals than tourists. But frankly, I'm fine with that: we residents are the primary users.
Improvements are certainly within reach. The Kickmap is a fine example. It grants each sub-line its own graphical designation, making it easier to grasp that (for example) the N-Q-R trains are largely interchangeable in Manhattan, but split into unique routes in the outer boroughs. Kickmap also offers both a Day and a Night version, making it easier to grasp the many confusing differences in service. (The MTA could also do a much better job with its in-station signage to make day-night differences clear.) But frustratingly, the MTA flatly declined to introduce Kickmap-style improvements a few years ago; just as frustratingly, Kickmap's creators appear to have dropped the promised Android version, so only iPhone users can carry it in their pocket.
But compared to the Underground map or Boston's (the other one I'm reasonably familiar with), the New York map is superior as a means of navigating not just station to station, but location to location. London's and Boston's fail at many points to make alternative routes clear in the event of a delay on one's chosen line or inability to easily reach the ideal line. If you can't catch or reach the 6 to Spring Street in New York, for example, you can easily determine from the map that the R to Prince will drop you off just a short walk away. That's often not so in equivalent situations using London's or Boston's maps.
No map is perfect, obviously (except for the one Borges envisioned!). But all in all, I prefer New York's approach to the one proposed here. Since we're on the topic, however, I'd also like to give a big shout-out to Mexico City's subway map, which in addition to giving each station a name gives each station an icon: either a graphical representation of the station's name (a rose for La Rosa, e.g.) or a well-known landmark, like a cathedral, associated with it. It's an elegant way of addressing the needs of locals who can't read or speak a language other than Spanish, and those of addled and anxious tourists. I'd like to see other systems adopt the practice.