I don't know if there's some bug that's going around, but a fair number of people have been out during Tony season, when traditionally no one is allowed to take vacation. I have to admit it makes me nervous about buying tickets in the hope of seeing specific performers.
I noticed the Drama Desks are on Tuesday, June 6 from 3 to 6pm, when I think most shows have Tuesday performances at 7. That does not seem like great timing to me, although Sardi's, where the event is being held, is not open on Sunday or Monday. I don't know if there's another venue that could have been tried. Last year, the Drama Desks were also on Tuesday afternoon, but they were not held until after Tony voting had closed.