(1) DARPA (and NASA) appear to be models. Secrecy and unaccountability are a big part of what makes them them. (2) The state of university grant making is currently terrible. A lot of what makes it terrible is accountability.
A agree with the premise that you need independence to pursue high risk stuff. The whole premise is investing in things that most people think it are stupid and will never work. That's just not compatible with standard accountability norms.
Meanwhile, as you say, contracts go to insiders regardless. It's not like FOI is preventing this corruption. I also feel that (at least on this thread) the British take on corruption is overblown. Was there ever a time or place where sleeping with the mayor of London was not good business? £100k seems cheap. Not saying this is good, just that I don't see the escalation that some here see.