No you don't, because there's no obligation for the ambulance officers to pick you up and take you. A taxi is in the business of taking anyone they can anywhere they can. An ambulance is not. The only time they'll
offer you a ride is if they judge that you may need of it, so already qualified ambulance officers have deemed you a possible candidate requiring their services. Moreover, they've only got one destination - the hospital - and it's not as if many people want to go there willingly. It's not as if you can call up an ambulance to pick you up and take you down to the pub for the night. If the ambulance officers are qualified to recognise medical emergencies (they are - that's their job) then they're qualified to determine who requires ambulance transportation and can filter patients accordingly.
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.