It sounds like you have an infallible instinct for exactly which lines of research should be funded and which are useless dead ends. The NSF should hire you immediately!
But he's not wrong, research really isn't just random playing (which I think is obviously still good and fun and should be done for it's own sake, of which this blog post is a great example though it probably wouldn't be worth the time of a formal research project).
It's the reason why "good questions" and seemingly arbitrary or trivial problems - especially those which motivates the development of much deeper machinery or discovery in order to solve them - is widely appreciated across all fields of math (poincare conjecture, galoi's proof of the unsolvability of the quintic, fermat's last theorem, riemann zeta's zeroes etc.)
In all cases those good questions where not randomly cooked up but posed from a previous, more direct line of inquiry, of which the originator usually had a good insight into. Though for the examples I gave the unexpected depth certainly could not have been anticipated beforehand.
always the problem with scientific research is that we never know why anything actually works the way it does, but we have a lot of ways of talking about it
There is no insurance redistributing credit amongst all of the pointless searches.
The guys who invented imaginary numbers or eigenvectors weren't just throwing darts at a board and got "lucky".