I get wanting to be with your family, but walking across that stage is literally a once-in-a-lifetime opportunity. I didn't walk the stage for college graduation or my ring ceremony, but I would absolutely be walking the stage at the draft.
I think they might help alleviate this by making it a more intimate atmosphere for the players. Instead of a large banquet setting, they should have dimmed lights, leather couches and somewhat secluded and closed off areas for those wishing for more privacy while they wait. No one wants that camera in their face the whole time.
I feel sorry for the guys that do attend this year. The place is going to be a ghost town backstage and the handful of prospects that are there, are going to get hounded by cameras.