Looking around aviation news and history, I see that many commercial aircraft are touted to have this or that much time fly between New York and London. What caused the route between these two cities to be used in measuring the "speed" of the aircraft?
They are (and historically, were even more so) two of the biggest cities in the business world (ranked Alpha++). That specific route has some of the highest rates of business travel and is, therefore, a fairly prestigious, famous route which is popular with fairly wealthy, prestigious people.
They are also two of the most famous cities in the world, and most people know roughly where they are on a map. The fact they're separated by an ocean which is large but was just small enough to be possible to cross safely in the early days of aviation also helped, because it gives the impression of being further than it is.
For example it's a comparable distance to London-Dubai, but that doesn't "feel" as big due to being overland through Europe. Equally while many people know roughly where Dubai is nowadays, it wasn't anywhere near as famous 30-80 years ago.
I suggest that the particular international air route is used because (1) both countries speak English and (2) English speakers read easily left to right.
I believe that commercial aircraft pilots and air traffic controllers around the world speak English at least as a second language.
The particular route is typically perceived to be longer than many other routes that are the same length yet nearer the equator. Perceptions can be misleading. For instance, on a Mercator projection map, Greenland appears about the same size as Africa, but actually Africa is 14 times the size of Greenland.
Once a benchmark is set up, it's usually preferable to add data to it and continue using it, than to create a new benchmark, because it permits a comparison between current and previous samples.
So even if the two cities are not the most logical choices now, they were in the past.
New York to London is a route which benefits from a strong tail wind - it takes 6 hours (British Airways, in a 777) in that direction, but 8 hours from London to New York.