First off, stop looking at "profit motive" as a bad thing. If the company doesn't make a profit, the many people employed by the company can't get paid. Profit needs to exist in order for things to continue. Would you go to your job every day if all it did was cover your costs of staying alive and left you with no extra money? Second, insurance is a gamble, both for the buyer and the seller. There's no guarantee the insurance you buy is going to completely cover you for everything. There's also no guarantee that the insurance company will collect enough premiums to cover all claims. Some years profits are big, some years they're small, and some years they suffer losses. Making the insurance a "government solution" isn't going to change any of this. There are still a bunch of employees who expect a nice paycheck at the end of the week. And there is still no guarantee that premiums will cover all claims. However, there is a big difference between a private company and a government department. Private companies need to run the business efficiently, because should they screw up, they're all out of a job. A government department, however, doesn't face this worry. This is why government bureaucracies become bloated and inefficient over time. Look at Canada's health system, where the average wait time from initial referral to actual treatment performed by a specialist is well over 20 weeks.
http://blogs.canoe.ca/davidakin/health/our-embarrassing-health-care-wait-times/#.Um6B9aRk1Uk.twitter And because it's a "universal" health care system, there's no accountability in terms of costs versus services delivered.