Yes, that is possible. I suspect, though, that many good, motivated researchers would be overlooked by more targeted approaches. Partly that is just because targeting one researcher necessarily excludes all other researchers. Partly it is because not every good, interested researcher has a lot of name-recognition. Also, a paper prize need not target a single academic discipline, and since the topics at issue are interdisciplinary, advertising a paper prize across philosophy, computer science, statistics, economics, psychology, etc. seems like a good idea to me.

But perhaps a better answer is to do a bit of both? SI could take a $20k investment and split it to do an experimental comparison. I, for one, would like to see an experimental comparison of the quality and quantity of research produced by a $10k focused grant and a $10k paper prize.