Answer primarily for Germany, then comparison with what I gather about mandatory car insurance in BC (feel free to correct me).
To me this doesn't make much sense, as in theory car insurance and disability/health insurance should be two completely separate products.
I think what is slightly misleading is that the car insurance is named after what creates the risk (operation of a car), whereas the disability/health insurance is named after what the risk is (disability/injury).
Note that the mandatory car insurance does not cover damage to the car (which one may be led to believe if one took car insurance in analogy to health insurance).
The mandatory car insurance (DE) is actually a pure liability insurance. And your liabilities include health damage you cause to other persons besides material damage (that's the connection to health insurance). Both are exclusively damage you caused others, your own car (DE+BC) and your own health (DE, BC see below) is not covered.
What are the reasons behind such policies?
I think the logical point is the liability: the mandatory (liability) insurances make sure that damage you (your car) cause to others is paid for.
Why not only have the drivers insure their car
For/aginst what exactly? Liability => that's the current status. If you want further coverage of damage happening to your car, you're free to insure that also.
and then let everyone purchase separate insurance for injuries?
Because in general our legal system (both DE + BC/CA) says that if you cause any damage to someone else, you are liable for that. Injuries/disabilities are not excluded, and your car is not treated specially: if you as a pedestrian don't look where you go and walk into someone who falls and breaks their wrist you are liable for that damage, just like you are liable for the damage if you accidentally bump into someone else, and break their glasses. Or if your dog's wagging tail causes your neighbour's 1-year-old to bowl over and fall on their head.
Cars are treated somewhat special as belonging to a class of things that are particularly risky - so that a liability insurance is not only recommended but mandatory. But liability insurance is mandatory for other risky things/activities as well (DE, not sure about BC/CA), e.g. for a hunting license you also need to have a liability insurance covering hunting accidents, and in some Länder a liability insurance for your dog is mandatory, you can follow certain professions only if you have a professional liability insurance, etc.
Several different/separate insurances may be involved with a car accident. Assuming you have an accident and are at fault:
- Your injury and rehab compensation in Germany is paid by your own health insurance (or your occupational accident insurance if you are driving for work).
In case you were not just at fault but grossly negligent (say, totally drunk), your health insurance may send you their bill afterwards. Your physiotherapist, however, can be sure they'll get their money for treating you - regardless whether the health insurance's bill will get you into bankruptcy.
In contrast, in BC, these costs are covered by the mandatory car insurance. So your car insurance may be lower if it didn't have to cover these - however, your health insurance would need to be correspondingly more expensive*.
If you (being at fault) cause injury and/or disability to someone else, you are liable. As with car accidents this damage can easily be far more than a single person can be expected to be able to pay, a liability insurance for the car is the mandatory car insurance in Germany**.
Likewise this is included in the mandatory car insurance in BC.
The same differentiating logic is applied to material damage: material damage you cause to others is your liability (and included in the mandatory car liability insurance both in Germany and BC).
Material damage you cause to your own car is your own. However, if you like you can buy an insurance against that (neither in Germany nor in BC included in the mandatory car insurance).
One remaining question is who pays if the liable party is not known (hit-and-run) or was illegally driving a car without insurance (uninsured/underinsured).
In Germany, all car liability insurance providers together provide a pooled insurance for injuries/disabilities (but mostly not for material damage). In BC, these cases are also covered by the mandatory car insurance.
* If I understand the insurances in BC correctly, there is only one mandatory car insurance provider and one health insurance provider (both provincial). In contrast,
in Germany there are many insurance companies who provide the mandatory liability insurance for cars and there are many different health insurance providers.
With only one provider in BC, it may be cheaper overall if the faulty driver's own health and rehab costs are also covered by the car insurance as otherwise assigning the costs correctly to health vs. car insurance may cause further costs that can be saved. Under these circumstances it doesn't matter much whether all those health/injury costs are paid for with your car insurance fee or with your health insurance fee - where you assign it is a mostly political decision.
Philosophically, the decision would depend on the weight you give to various thoughts:
- that operating a car is inherently dangerous, even with the ideal driver (damage to driver => car insurance)
- and that better driving usually/often doesn't prevent accidents (damage to driver => car insurance) or
- that getting yourself into accidents of all sort is rather a general risk in life (damage to driver => driver's health insurance), and
- that possibly the higher risk of operating a car is already sufficiently punished by your pain, which after all, money doesn't really compensate (damage to driver => driver's health insurance).
**One may reasonably argue that the driver rather than the car should have the insurance - I guess requiring it with the vehicle is a practical decision: drivers may change frequently, but without the mandatory insurance you don't get a license plate (or in some other countries a sticker/sheet that you pin to your windshield) so that missing insurance is easy to spot for police etc.
Also liability insurance fees go with annual mileage which is easier to know for a car than a driver.