north of Central Park many stations are unconnected but similarly named).

And south of it also. But "similarly named" is a red herring. London
comes close to a one-to-one relationship of stations and station names,
but New York doesn't believe in that; the names are only supposed to be
unique along a single line and then only within a single borough. (The
R train stops at 36th St. in Brooklyn and 36th St. in Queens, passing
through Manhattan in between, where perhaps fortunately there is a 34th
St. station but not another 36th.)

And no-one's seriously confused by 23rd St (C)(E), 23rd St (1)(9),
23rd St (F)(V), 23rd St (R)(W), 23rd St (6), and the future 23rd St
(T). There's also a 23rd St station on the E and V in Long Island
City, Queens. This is called 23rd St - Ely Av. There is no Ely Av
anywhere near the station - it's just what 23rd St (Queens) used to be
called before the Queens street numbering of circa 1920. The IND only
put the second name on the signs to avoid confusion with the much
better known 23rd St further down the line in Manhattan!

If London named stations the way New York does, Tottenham Court Road
station might have had that name on the Central Line but been called
Oxford Street on the Northern, while Warren Street station on the
Piccadilly might have been a second Tottenham Court Road station. But
even if that had been the case, it wouldn't imply that the interchanges
should be any different from what they actually are. And analogously in
New York.

And if NYC didn't you'd have the Fulton St Line in Brooklyn crossing
under the East River and stopping at Fulton St station in Manhattan.

(doubling back at 145st will almost certainly involve exiting
and re-entry, as it does at most stations),

I don't know about 145th St., but probably not. The reason New York
has stations with two separate fare-paid areas for opposite directions
of travel is that they wanted the platforms to be accessible from the
sidewalks and only one level down from the street (to minimize stairs).
If they put the local tracks in the middle, between the express tracks,
a single island platform would suffice, but it would need to be accessed
from the middle of the street, as in Berlin. Once outside platforms for
local stops were decided on, the only way to allow doubling back within
a single fare-paid area would be to add a subway (in the British sense)
connecting the two platforms, like at Queen station in Toronto, and this
was evidently felt not to be worth the cost and trouble of building.

145th St on the A, B, C, and D has got a full mezzanine (and therefore
you can change direction there). 145th St on the 3 hasn't even got
platforms long enough for the train, but I don't think you'd want to
go there (with regard to the Lenox branch of the 3, the first place
where you can transfer to an Uptown 2 train is at 110th St). 145th St
on the 1 and 9 also has no passenger crossover (but again, why would
you want to?).