have some sort of Common Law responsibility to actually look after their Customers? Something like a Duty of Care?
Yep - but duty of care extends to customers who are in your premises or using you product or service. The only thing forcing any company to look after its customers outside the bounds of warranties/contracts (like the Ts&Cs most passengers agree to but don't read) is retention of market share (goodwill).
For some airline models, this is less important to profitability than other drivers (maintaining a low cost base etc.)
The problem here is not what the airline should have done, it is in the perception the travelling public has of what is reasonable. At no point do we tell them that "When you buy a ticket, we take that as our responsibility to get you to your destination by whatever means necessary". No airline can maintain that degree of assurance, yet most passengers seem to believe this is what they are paying for.
The only way to get the type of service these people want
guaranteed ...... a First Class Ticket with a boatload of travel insurance.