There is always an opportunity cost incurred when personally saving up money for emergencies, but at least you have the principal if/when the emergency never occurs.
However, if you had paid that money out to the insurance company rather than saved it yourself, then you lost both the opportunity cost and the principal.
Those two aren't exactly equivalent, an insurance wouldn't cost nearly as much as the amount you need to save for emergencies. Saving money to mitigate an event that only has a 10% chance of happening requires 10 times as much money than you'd need on average. Even if an insurer asked twice as much as necessary that'd still leave you with 80% of the money free to spend, rather than 100% of it locked up in a savings account just in case.
Ah, so we all give it to the insurance companies...who invest it for us and keep the profits from that for themselves? Why not just e.g. Maintain and ETrade account with enough to cover e.g. Vehicle minimums? In California at least, you can provide proof of financial responsibility in the form of a $35k deposit with the DMV or a $35k surety bond: https://www.dmv.ca.gov/portal/dmv/detail/pubs/brochures/fast...
So your suggestion is to give even more money to the bank so they can invest it for you and keep the profit to themselves? Except in this case you end up paying for all damages. I'm not quite seeing the point of your argument.
Also, my knowledge on Canadian car insurance policies is severely limited, but if you can fulfil your insurance requirements by setting aside a lump sum of money, then I'm assuming you're either still liable for all damage over $35k, or the Canadian government will cover that part, which is still an insurance, except you pay it through taxes.
However, if you had paid that money out to the insurance company rather than saved it yourself, then you lost both the opportunity cost and the principal.