G&T is right about Bermuda. In the 70s BA operated a daily 747 between JFK & BDA & less frequent 707s to Barbados. Other European carriers operated from JFK to their colonies or ex colonies in the Carribean.
It is interesting to look at 1970s timetables. Long haul flights had far more intermediate stops than you you would get these days. Swissair operated a substantial programme via Athens. PA & TWA operated Rome - Lisbon - JFK (and generally a few other stopovers). Indeed SR operated a flight to JFK via LIS. TWA had a large number of intra European sectors even if the final destination was also served non-stop.
I think that it was a combination of a legacy from days when aircraft had a very limited range, an unwillingness to give up routes (flying was very much a matter of national prestige and it took things like the fuel crises of 1974 & 1979 to change things), and a lack of adequate point to point traffic.
I do seem to remember that BOAC had its own ticket office in cities such as ZRH rather than use the BEA one doubtless a matter of prestige.