I have been a British Airways Gold Card member for the last 15 years straight, and almost every year other than that since its inception in 1990 or so when it was a paid lounge program, and I do not live in the UK, so forgetting what everyone else complains about, I speak from experience when I write about the transfer experience at LHR. Furthermore the dining options are much the same at 5 as they were at 1 or 4 (yeah there are a few more restaurants, whoopee.........again, I know no VFF's who really use these) and you will see that everyone laments the fact that T5 is a shopping center which gets in the way of serious travellers.
In any case, as BA's passenger count has gone down from over 40 million passengers just a few years ago to under 30 million passenegers now, AND the majority of their passenegers are connecting passenegers while the numbers at each hub you cite have INCREASED for O/D AND connecting pax, it would seem that many do not agree with you (and yes there are factors like UK tax to consider, and BA chopping certain destinations, decimating its domestic network, etc).
Regarding your thoughts on connecting at JFK or not, what Continental does or does not do really has nothing to do with it. CO until the merger had almost no presence to speak of at JFK and barely existed at LGA, while DL is a big player at JFK and LGA and a medium player at EWR. Furthermore with the acquisition of NW, DL offers a lot more point to points from Europe to the US, so connecting traffic may in fact be down and stay down.