CRP5,
I think you'll probably find that three airframes are needed for the LHR-JFK run to allow for a morning flight (out am, back pm), an evening flight (out pm, back the following am) and a spare. Certainly when services operated normally, there was a spare airframe available in case of unserviceability. It's amazing what £5000 per seat can do!!
As far as it being an 'unreliable heap', it operates in extreme conditions of stress so it's very likely to need a bit more TLC than your average airliner.