I'm sort of furious because
1/ I expect the counterpart of my loyalty to be a kind of "we treat you as a human not a machine" attitude, and BA sounded horrifically bureaucratic from A to Z -- what if I have a bigger problem? Will they be understanding and helpful? and
2/ arriving near the cut-off time happened to me a few times in the past, including arriving one day after departure on a super cheap LH Y ticket, and they always got me on board for free or a nominal fee.
1) If you have a bigger problem, such as? Missing a flight due to hospitalisation? Covered. Death? Covered. Act of God? Pretty much covered.