This is a crazy thought but the government or charities could award a random lottery to good-Samaritans? Then suddenly everyone will want to help. The only problem is this will also cause fake incidents for fraud purposes. Or people who purposely cause accidents to "help". But if they can solve that issue, might work?
Currently if you report an accident or get the injured person to a hospital you'll be treated as a witness and have to attend all court proceedings. The law should differentiate between a samaritan and a witness (unless the samaritan also wishes to be treated as a witness).