Well these are my thoughts (generally)
Healthcare should be a right granted to everyone, thus the single payer system. The government should provide an essential level of healthcare to cover the needs of everyone. Go to any doc you want, everything is subsidized centrally ($5-$15 copays!). Docs get paid, people get the healthcare they need. However if you opt for a "better level" of healthcare and you have the means to do so, then by all means go find some superstar doc that is paid privately. Don't tie healthcare to business benefits. Businesses have other things to worry about and they can focus on that instead if their workers are healthy!
We did study the US healthcare system in some depth (economics class) while I was in college (back in Singapore) and it seemed to me, from the data, that insurance is the main factor driving up the healthcare costs. Because the cost to the patient is just a deductible, the healthcare providers are able to jack up their prices without the patient (customer) feeling the pinch!
Assuming that healthcare costs go to a single-payer system run by non-profit government agency, will they stand by and deal with such insane prices set by the healthcare providers? No, they will set up some form of schedule which determines what is reasonable (e.g. cold/cough/flu - $100, wellness checkups - $120, broken arm $2000....you get the idea). At that point, let capitalism take over - the money is there and so if the docs want to provide the service at the specified cost they are free to enter the trade... otherwise they leave and find something else to do.
I know it's hard to tie efficiency and government in the same sentence....then again who will manage the centralized healthcare system?
-S