You could probably waive charging direct costs if you had some other way of deterring abuse, but they essentially always have to respond to 911 calls, so the only way I could think of doing so would be to arrest someone who misuses the service. A policy of informally losing the bill for legitimate calls might work, or doing the standard drug dealer "first one's free" strategy. But I don't think $100-500 for an ambulance would break most people, particularly with insurance; a charity could also cover the bills for some people.
The problem with 'a charity covering the bill' is that you then need people to donate out of goodwill. That doesn't often happen.
There's already fines and punishment for abusing emergency support systems (e.g.: calling 000/911/your country's equivalent). Even if you abuse that, and even if you mislead the call centre operator to dispatch an ambulance to your house, they're not going to ferry you to your desired location unless your vitals show reason to consider it a possible requirement.
Ambulance services are free here, insofar as you pay for a small tax on every rates bill (said rates cover ambulance and waste management services) edit: Apparently not since 2003 - it's now simply just covered by the State. There's no out-of-pocket expense. I can guarantee you that we don't have ambulances running people not requiring their services around 24/7.
And, if they're evaluating you on scene, even if they decide not to transport, they've already rolled the truck(s) to see you, which is probably much of the cost.
As rdl pointed out, the liability is just too high to refuse to take someone to the hospital.
However, it wouldn't surprise me if the liability issues were very different in the UK.
There's a separate argument about who should pay for what services, but "care should be delivered in the most cost-effective way to get the best patient outcomes" is independent of that.
Lots of 'fall down go booms' and 'they just aren't acting right' (yeah... it's called 'getting old')
There probably should be a cheaper way to treat them than sending SF Fire over and over to the same addresses. And that way would probably be both more comfortable for the patients and lead to better long-term outcomes. Maybe more extended inpatient care for them (in a low-cost-per-day facility)?