If these brilliant scientists/professors are not (adequately) financed for their research, inevitably a large part of their time will be dedicated in looking for funds, detracting it from the time dedicated to the research itself.
So, not only some research is not possible (or gives scarce results) because of the lack of funds, but the time spent in looking for other funds will reduce the research results in a perverse spiral.
In a perfect world research institutions should be able to make their lead researchers "worry free" (about the funding and the other bureaucracy matters), as this condition is the one where creativity and productivity is at the top level.
Since funds are obviously limited, maybe the issue is about starting too many researches (underfunding each of them) as opposed to choose a limited number of research projects and fully fund them.
But if you use this approach, the issue becomes the war for being selected, the possible corruption (or simply bad judgement) of the selecting commission, etc.
I guess noone has a proper solution to the issue.