TLDR; No. See Soviet Union.
Why should it? The free market is the most powerful incentive there is. Government control of the pharmaceutical industry has been tried before, in the Soviet Union and it was a mess.
Here's an excerpt from Michael Binyon's "Life in Russia" (1983)
"How often are foreigners asked by Russian friends to bring back drugs for sick relatives, and how often does the press complain that cheap, effective Soviet drugs are simply unobtainable! Take the case of a researcher who discovered an efficient drug to stimulate growth and spent fifteen years trying to get it on the market. In spite of repeated clinical tests, scientific endorsement and an urgent demand from people with deficiencies in growth hormones, the drug was unavailable. Instead manufacturers were producing a less effective foreign product which first came on the market twenty-two years ago.
What is on sale in the shops or in special kiosks is so outdated or so general in its effects that few people buy the product. Packets of good pills are so valuable that they are sold at special foreign currency counters in tourist hotels. Doctors issue prescriptions even if the hospitals have no supplies, leaving it to hapless patients to use their wits in trying to get hold of what they need. There are plenty of stories of dentists working without adequate supplies of anaesthetic, of polyclinics unable to supply a full course of treatment, of chronically sick people living from month to month, never sure whether their prescriptions can be renewed.
The drug industry suffers from none of the failings its Western counterpart is accused of: there is no risk of profit-taking at the expense of safety, no aggressive marketing of unnecessary drugs, no costly duplication of research laboratories. Instead, research, development, testing, approval, manufacture and promotion are organized as a public service. But the links between each stage are so weak that the time lag between research and retailing may be up to seven years. Responsibility for pharmaceuticals is divided between the Ministry of Health and the Ministry of Medication Industry. Everything used to come under a subdivision of the Ministry of Health, but because of poor results a separate ministry was created in 1967. The Health Ministry is still responsible for resarch, testing and licensing of new drugs. The new ministry deals with production and quality control. Most research is carried out in state laboratories, and if an effective product is discovered it is sent to the Ministry of Medication Industry which finds a suitable factory to try it out. Test batches go back to the Ministry of Health for clinical trials, and often, if approved, to another plant for mass production. A separate agency handles distribution and marketing, and quality control is the responsibility of an independent state inspectorate.
Theoretically each stage leads to the next with no waste or duplication. In practice the chain becomes a bureaucratic nightmare. The institutional separation means that each body operates according to its own terms with little concern for the total process. By the time the product gets to the chemists' shelves, it has often been rendered obsolete. Research institutes have no real leverage to press factories to put their results into production, and have little incentive to do so. As for the manufacturers, they cannot get back their initial production costs because of a rigid pricing system, and find it cheaper and easier to stick to the older and tested lines for which there is already a market.
The lack of advertising means that doctors are often unaware of what is available. Sometimes they prescribe drugs that have long been withdrawn from the market. Similarly, since brand-names play little part in the pharmaceutical industry, a factory manager is not too concerned about the name and reputation of his plant, and this breeds indifference.
The Russians have tried various remedies. The simplest is to import drugs."
Gilead spends almost a billion dollars PER QUARTER on R&D expenses. Amgen spends over a billion per quarter, Celgene spends 1.3 billion per quarter. Most of those discoveries that come from those expenditures will never see the light of day. So how else are they to recoup their costs? If the government started funding pharmaceutical development at the tune of 25 billion per year, how would that infrastructure suddenly be created? Would they also need to get into the manufacturing side as well? Manufacturing many drugs is not a trivial process. Then there's the marketing expense -- doctors would need to be aware of the new drugs. There's distribution involved. Getting the government into the pharmaceutical business would be a massive, massive expenditure and still result in lower quality than the private sector could produce because the competitive forces would be eliminated. See the success of pretty much any Iron Curtain industry compared to the US and Japan for examples of how this goes bad and ultimately results in lower quality. Can you name a single Russian electronics manufacturer that you can buy in the Frankfurt Duty Free shop?
Of course the argument would be "we can do it more efficiently than the Soviets" -- sure. That's the same argument Communists use to suggest that "this time it'll work." I'd rather trust my life to someone that will profit from my survival than to a government that is influenced by whatever political forces are at play. Then you have the issue of what drugs deserve public funding and what drugs do not. That becomes a political decision and not a market decision. That's very dangerous.