That public funding has to come from somewhere, though, to the tune of quite a few billions of dollars. Do we really believe the tax increases required will be palatable to voters, and politically possible for elected officials? In the US, we can't even get universal public-funded healthcare.

Not sure the increased secrecy would help all that much. Is drug manufacturing that complicated that a motivated company could not reverse engineer a new drug solely from its off-the-shelf product, without too much trouble?