There should first be a good base of teaching assistant funding with enough free time to do research work. A lottery for extra PhD grants would indeed work well

There should first be a good base of teaching assistant funding with enough free time to do research work. A lottery for extra PhD grants would indeed work well on top of this. Often the key is simply top-k grades now for those grants. Fun fact, most historical republics and democracies elected political offices by lottery. https://en.wikipedia.org/wiki/Sortition https://en.wikipedia.org/wiki/Sortition