Would we be seeking compensations from BA or any other airline for that matter if we accidentally left our iPad in the seat pocket, on the basis that BA should have reminded us? Our own forgetfulness is our own responsibility. In this particular case you've admitted that you knew about needing to collect your luggage and re-check them but you forgot. I do not think it would be reasonable to expect BA to compensate you for your own mistake just because they did not remind you.

An airline should not be held responsible for our mistakes - should they tell us to turn up on time for our flight in case we forget, and pay us compensations for not reminding us if we forget?

Saying that, I'm fairly sure that a PA is made on a BA flight into SYD to collect our luggage if we are connecting onto a domestic flight even if our bags are tagged to the final destination. I cannot remember if they do that on a flight to the US but I'd have thought they do? They might even make PAs at the baggage hall like they do in various other countries.

We need to take personal responsibility for our own forgetfulness etc - it's nice when other organisations/people remind us, but ultimately we should be responsible for our own actions or inactions and not try to blame anyone but ourselves when we do know something already and we forget.