Are you aware of any implementations of that lottery model in the wild?
The usual argument against a lottery is it does not reward the best scientists and will give grants to third rate hacks. This is true, but it can be solved by having different lotteries with different thresholds. Publish one paper in the Journal of Useless & Pointless Results and you go into Pool A where you might have a 0.1% of getting a grant. Publish 20 articles in Nature and Science and you go into Pool H where you have a 75% chance. We would just need to be careful that we are not recreating the same perverse incentives that the current system encourages, but this is not insurmountable.