They do. But they focus on the earliest stages of drug development, mostly involving proofs of concept. That doesn't solve the problem of actually getting the drug approved so that it can be used by patients - which is where the costs skyrocket.
As a non-American, why do costs skyrocket in the approval phase? Is it that the drugs have to go through multiple rounds of clinical testing over years? I struggle to understand the astronomical price tags, but I'm assuming it's something bureaucratic?
I think it’s just because of the degree of failure. Going through the rounds of clinical trials might cost £15m, which isn’t much amortized over drug sales, but you might go through 50 candidate drugs that fail (and possibly at the last stage of clinical trials after the money has been spent) before you get one success. Public or academic research bodies don’t have the capital or the appetite for risk to go through that process.
I think there are quite a few drugs which work exactly as intended, except for the small detail that they turn out to be toxic to humans. One of the big outcomes I’m hoping for from stem cells is to be able to test heart or liver toxicity before human trials, weed out a whole subset of failures before substantial money is spent, and make the whole process of drug discovery inherently more efficient.
Part of the reason is not bureaucratic but that clinical testing simply takes enormous amounts of labor, since you need to do it at a large scale.
Alternatively, you could say that the requirement to do that much clinical testing is an arbitrary bureaucratic decision and could be lowered - but there are political reasons (e.g. thalidomide) to err on the side of caution even if extra testing saves less lives than it costs lives because of the delays.
Drugs are tweaked during development. The initial candidate compound is more for proving that a particular class of drugs has promise. But tweaking for toxicity, effectiveness, etc. can only be fully done in clinical trials.