I'll flip this around and say I've never understood why an airline is viewed as a special case. In the general case, if you enter into a contract and pay for a service, then don't receive that service, you're entitled to sue the service provider for your losses. For example, if I turn up to a hotel I booked only to find that the room isn't available, I'm entitled to sue the hotel for my cost in finding a reasonable last minute replacement. That's the case even if the room wasn't available because it was unsafe for some reason.
Of course nobody is expecting that they "keep flying the plane with engine issues so you could make your important meetings". But ultimately you relied on them to get you to that meeting, and they failed to do so, so you should be compensated so that you're no worse off than if they had provided the service. The fact that an airline will sometimes fail to get their customers to their destination and will have to compensate them for it, is just the cost of doing business.
Luckily in the UK and the EU your right to compensation for delayed flights is enshrined in law.
Of course nobody is expecting that they "keep flying the plane with engine issues so you could make your important meetings". But ultimately you relied on them to get you to that meeting, and they failed to do so, so you should be compensated so that you're no worse off than if they had provided the service. The fact that an airline will sometimes fail to get their customers to their destination and will have to compensate them for it, is just the cost of doing business.
Luckily in the UK and the EU your right to compensation for delayed flights is enshrined in law.