Research grants in the U.S. (and many other countries) are so competitive that many, many good ideas go unfunded. When funding success is at 10%, many researchers think applying for a grant is just rolling the dice. Obviously, there are certain things that can improve the likelihood of getting a grant, but there seems to be a large component of luck in the process now.
Why not just admit it and award some grants through a lottery system?
They do it for green cards in the United States.
Obviously, there would have to be some criteria to insure that grants do not go to poorly written proposals. Make them small -- micro grants, even. Make them just as accountable as large grants.
It could help ensure greater diversity of ideas (just like the green card lottery helps promote diversity). It would provide insurance that “old boys networks” and coalitions of researchers don't have complete control over the review process.