Yes 'The Government' with a wave of its magic wand could solve all our problems. The only reason they don't is because they're bastards.
They could adopt a policy of taking action to stop all preventable deaths by any cause. It would mean bringing the world to a halt and everyone stopping alone in their bedrooms forever. Even then some people will still manage die by some avoidable manner, electrocuting themselves or starting a fire or something.
Taken to its logical conclusion it makes no sense whatsoever. Life is full of risks, we take our chances.