This answer is probably limited to the US. You have a misunderstanding about NSF and probably other funders, such as industrial organizations.
The NSF funds projects not institutions (except indirectly). NSF depends on the fact that it need not provide basic salary and benefits for those it funds; the universities (and such) provide that since such institutions have multiple goals, not only research. But the NSF will provide funds for specific things proposed to it by individual researchers provided those things seem to have scientific merit.
I question your "more informed decisions" statement. It is the individual researcher that knows what is needed both in terms of funding and in terms of what is likely valuable to attempt to explore. Someone up the chain (deans and such) have more general responsibilities and don't normally get involved in the nitty-gritty of actual research. So, if the NSF (etc.) depended on administration for proposals, then two bad things would occur. First, the proposers could likely only make general appeals (Trust us; we do good stuff), and an extra layer of separation would be placed between the people with the ideas and the people with the funds to support those ideas. The researchers would still need to "apply" for funds, but to the administration, rather than directly to NSF.
Your second proposal (independent labs) would require much more funding. MUCH more funding. Universities provide both basic salaries, and the buildings in which those researchers work. NSF funding covers quite specialized things that may be (in the current political environment) beyond the ability of universities to fun. The university provides the "general" funding. Foundations provide the specialization.
Also, peer review works in the current scheme, since people at other institutions are willing to review proposals in their own fields. This gives a variety of viewpoints. If the NSF funded institutions rather than projects, then that would be lost. Each university could, I suppose, develop its own project review system, but it is hard to see how it could attract the same breadth of view or be reasonable to fund itself. It would add to the cost since it is more balkanized.
Companies can fund projects internally since they have a much narrower view (often product based) than a university (the "universe" in "university") does.
Startup companies with a new perspective need a lot of funding if they are to have a chance and the failure rate is high. It is very risky for funders, especially those in the basic sciences.
Orthogonally, researchers being required to get their own grants imposes a certain discipline of thought on them: a good thing. They have to be clear early on about the goals and the requirements. Clear enough to convince their peers of the value. This is also present in other schemes, of course, but it keeps researchers on right path since it requires justification prior to the research and also reporting afterwards.