The issueis that an ambulance is a mobile treatment centre as well as a transport device, it has some rescue drugs, oxygen, IV fluids to maintain blood volumes etc, so treatment can start on the way (and pain relief).
In some areas they carry nebulisers so asthma can be treated without the patient needing to go to hospital (which is quicker for everyone and frees up the ambulance quicker).
I've been in an ambulance twice. Once with back/neck pain after an RTA (got rear ended on the motorway - funnily enough my car wasn't drivable at that point...). Was fine but definitely needed properly checked!
Other time was for DS who had breathing difficulties with Chicken Pox, plus temperature not responding to calpol, (ibuprofen is contraindicated in chicken pox). Ambulance largely came to triage (it was midnight on New Year's Day) and they generally don't like parents driving kids with breathing difficulties because of the whole distraction causing accidents thing... Turned out they also didn't like the lung sounds so we got taken in and went straight from ambulance to cubicle to limit the spread of chickenpox among sick patients. We could have driven in but were asked not to to limit the infection risk. Would have been easier to drive as getting home would have been a lot simpler.
The midwives at the antenatal stuff said to call an ambulance if you were at the funny noises stage of labour as they'd also rather not deal with an RTA as well...
I'm horrified by the idea of people with chest pains or severe pain driving themselves - they could easily kill other people by being distracted (or passing out at the wheel).
Definitely need to throw money at social care in the first instance, plus mental health services in general - that should improve the rest of the service massively if prompt discharges of medically fit patients can happen and MH crises can be averted.