If only it were that easy. Remember when Medicare Part D was being debated and everyone thought "oh if we make it so Drug companies have a single payer from the government it will save costs" Drug prices havent gone down for seniors. Their is an inherent problem with just saying whatever you are paying now just has to go to the government. For most of the commercial business companies pay 75% - 80% of premiums. If you tried to regulate and say oh you now have to pay what is essentially a tax on what you were giving as a benefit companies will find ways to get around it. A lot of companies are also self insured so it would be really hard to keep tabs on what the were paying. The old saying of "you build a better mouse trap..." is applicable.
The reality is if we go to single payer like Canada we are going to have to ration care. Whether that is by panels or pricing it will have to happen. Additionally, one of the strongest lobby groups (The AMA) would fight everything tooth and nail. Cutting reimbursement to physicians would be a long ardous battle. Every year they try and cut the Medicare Fee schedules and pass a silly bill only for it to be rescinded when the budget is passed. IMO the only way to straighten this out is give people skin in the game and let them push the market. But it has to be everyone person with skin in the game. Only then can market forces push prices down. The incentives hospitals have right now is to keep builidng new stuff.
I've mentioned my plan before but I'd like to add some things to my list:
Medical school, Nurse Practitioner and PA schools tuition is capped at $2k per year. Most universities are not for profit and get a massive benefit from the government. If we are going to cut physician's pay we shouldn't make them take out 500k in loans to become a doctor.