Note that the government giving companies money doesn't mean the government magically owns any rights to the medication.
Are you proposing the government should have no attached requirements to qualify for subsidies?
Are you flatly against all regulation when a particular company is given tax money?
For what it's worth, the government can regulate any industry regardless of whether it is subsidized.
The price is actually set to where profit is highest, meaning it's a function of: how many people will buy at various prices and how much does it cost to produce at various quantities.
One of the strong arguments for single payer healthcare, IMHO.