We've already seen how that works; the money is given to the shareholders of insurance companies rather than to the policyholders in need of medical care.
The government does not need to make a profit on healthcare, which is why people are turning to them. (Plus, we've seen this system work in other countries. The US will not be the first country to give everyone healthcare; it will be one of the last.)
Depends on how you define 'work'. Nationalized healthcare where tried has delivered better results in some dimensions, worse in others. Those countries often rely on medicines and procedures pioneered in the USA's more open medical markets; if we give up that role, who will pick up the slack?
The government does not need to make a profit on healthcare, which is why people are turning to them. (Plus, we've seen this system work in other countries. The US will not be the first country to give everyone healthcare; it will be one of the last.)