To a first order approximation the job market is a market for lemons (jobs and workers). Generally, the best folks will spend the least time in the job market, if any at all (note that I said generally, there are exceptions which I'll get to, don't write letters). If companies make comparable offers but one requires a bunch more hassle and delay through an audition process then economics 101 says that people are going to choose the option with less hassle more often than not.
An audition is a cost, and without something to offset that cost most folks will simply choose to avoid paying it. If you really want to hire the best and brightest and you have to rely on an audition process then at least consider paying above average for the period of the audition and for the job (if you actually are getting the best and brightest, paying them above market should be expected anyway).
Alternately, look at other ways to hire. If you truly want a company filled with the best and brightest then I suggest you switch from a "filter bulk submissions" model to a talent scout model. Don't look to fill roles, just continually be looking for new talent, and form relationships with talented folks whether or not they're looking for work right then.