But in reality, the weather limits they are obliged to operate to means that, day or night, they are often not able to give that additional service the public might expect in all weathers.
Everyone expects the RNLI to go out in all sorts of horrendous conditions (and they do) so all that fundraising does provide a true emergency service 24/7 - I suspect the public belief is that their donations go to provide the same level of service from an air ambulance which certainly can't do what a SAR aircraft can.
I'm not expecting AA to operate to SAR limits but I bet that's what a lot of the public think they do.
Air ambos are excellent for the heli industry but throwing public donations at a limited capability is wasting money that should be spent elsewhere - other bits of the NHS for example.