As I'm sure you could guess, the reality is much much more complicated. Drug dev is really hard, and really expensive. Private money funds an order of magnitude more R&D than the government. That private money takes a huge amount of risk, and most investors lose money (even in the last few years when VCs and public equity investors have made money, those profits will probably be offset by poor returns to pharma companies for their expensive acquisitions of risky assets). The actual rent seekers in the US healthcare system are large hospital systems, although that's not something that is discussed much in the public debate (hospital spend accounts for 30% of US healthcare spend compared to 10% for prescription drugs, and the strategy of hospitals the last decade or so has been to consolidate into local monopolies so they can capture market share and drive higher rates with payers -- pretty much the definition of rent seeking)
Drug company R&D productivity has been declining for years, and probably will be zero or negative in a decade barring breakthroughs. From my limited experience working with NIH and FDA, the government would be way, way worse -- there is very little accountability so simple things are really hard and slow.
NIH spends ~$34B on R&D. Private industry spends over $200B (mostly US pharma companies, with a good number of EU and some Japanese as well). Top 15 biopharma companies spend like $70B per year on R&D in aggregate. Global venture funding is on pace to be $15-20B this year for biopharma
Despite all this money, we got 47 new drugs in 2017 in the US. Most for cancer and rare disease, because those are the only remaining therapeutic areas where you have enough of a shot of making money to attract private capital. If you look at the top 10 causes of death in the US, only one -- cancer -- receives much private funding and new drugs -- very few new drugs for diseases like heart disease, diabetes, mental illness etc. That doesn't even account for the world's most devastating diseases, many of which receive very little funding and innovation, because the economics dont work
To replace for-profit R&D with government R&D in the US, we'd need to probably quadruple or quintuple the NIH budget -- assuming NIH is just as efficient as private industry. If we wanted to allocate spend to the biggest unmet medical needs rather than those that can make a profit, we'd probably need to spend 10x the ~$300B+ the world spends now on drug R&D (that's basically a guess but I don't think it is crazy directionally, considering how little investment goes into cardiovascular disease, psychiatric disease, infectious disease, stroke, pretty much anything other than cancer)
Apologies for the rant and i know this is an unpopular opinion, but I think the public debate on drug pricing and healthcare costs in general is way off and is a huge obstacle to actually making healthcare better and developing new medicines