The 3 airline rule does not apply to Chicago, Los Angeles, New York City, and Boston, as they are much larger markets, and it only applies to the four Heathrow airlines (BTW, United ends Boston-London 28 October and British Airways ends Charlotte the same day). It's best briefed here:
h) Each country may designate only TWO routes on which TWO of its carriers may compete. Every remaining route must have only one carrier from each side. However, if the number of passengers carried TOTALLY on the route (including traffic carried by fifth freedom carriers Air India, Air New Zealand and Kuwait Airways) exceeds 600,000 in two consecutive years, or if the number of passengers carried by any single airline exceeds 450,000 for two consecutive years, then each side may designate an additional airline to serve the route.
However, not even that part fully explains it. But simply put, only one US carrier can serve San Francisco-Heathrow, as well as Miami-Heathrow.