Undirected research is quite possible outside the university system. Perhaps you've heard of Bell Labs? When the government still subsidized them [1], they did plenty of undirected research. In the university system, about 50% of the money the government has earmarked for research is actually used for that purpose. At Bell Labs, the number was close to 100%.
Most grant supported research groups do plenty of undirected research, and the NSF rarely objects when a project makes discoveries not listed in the grant proposal.
You are telling me that (roughly) doubling the amount of money devoted to research will harm research? I really don't understand the mechanism by which that would happen.
"If you can only do, no one will benefit from your knowledge."
Let me be very precise, since you seem to want to misinterpret what I wrote.
A researcher's skill set: generating new knowledge and spreading it to other researchers, and eventually practitioners. This is done through published papers, presentations at conferences, conversation and source code. Generating new knowledge is the primary skill here - other researchers will usually go to great effort to understand it.
A teacher's skill set: understanding existing knowledge and spreading it to people with no background in a classroom setting. The primary skill is motivation and understand people very different from you (e.g., premeds who hate math rather than other math Ph.D.s), and maintaining discipline. The goal is to convey existing knowledge, so creating new knowledge (the primary skill of a researcher) is more or less irrelevant.
There are not that many people who have both of these skill sets. I only had the researcher's skill set, and I know many people with the teacher's skill set.
Also, by "waste", I was referring to general university waste - overpaid and under worked administrators, duplicate offices, etc. If you ever work at a university, you will realize how wasteful they are.
[1] I believe the system was that every dollar AT&T lost at Bell Labs was deducted from their tax bill.