If people are not injured, you and I do not have to pay for their health care (although removal of medicare would fix this).....and if I die on the road, they will close the road slowing you down
If you go down the utilitarian road (and accept public healthcare) then you must also weigh other considerations. For example you are saying that:
Cost of healthcare for injuries > cost to society of complying with laws
However while the healthcare cost is quantifiable the compliance cost is harder to quantify. If for example not complying would save 100,000 people 6 minutes of time then that is 1.6 years of productivity, and then you keep adding on all the other costs of compliance (environmental impact, cost of helmets/seatbelts/whatever, etc etc).
And of course you also need to give more thought to the healthcare cost. You need to consider the value of human life (assuming that the intervention will prevent deaths). And then you need to look at the expected value. Which means the probability of the event actually occuring multiplied by the cost. For example:
Injury costs $50k however is expected to occur only 1% of the time, this means a $500 expected value.
Once all of these calculations are done and only then, could you actually compare the compliance cost to the healthcare cost.