It won't matter if BC opens up to private companies to sell compulsory/basic insurance.
Every year I go to renew, I shop around to see if I can get a lower rate on my optional coverage (additional liability, collision, comprehensive and rental coverage). Never have I received a quote where going private was going to be cheaper for me, and I am 15 years claims free, no tickets or violations etc. I therefore highly doubt that private insurers could offer basic insurance for less than what ICBC could. It simply isn't profitable for them.
The fact is that the private insurance companies will still have the same pressures that ICBC is experiencing such as rising injury claims, more costly repairs, high litigation and more cars on the road as urban area get increasingly developed and the population increases.